; E7fl TOM CO O CQ >- 'CANBUdKCOMWlNY G. A. SHERMAN, Druggist and Stationer, Main St., - Martinez, Cal. LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Received Accession No. & 7 . Class No. 3 If. ECLECTIC EDUCATIONAL SERIES. KAY'S NEW TEST EXAMPLES IN ARITHMETIC BY . DE BECK, A. M. NEW-YORK : CINCINNATI : CHICAGO AMERICAN BOOK COMPANY FROM THE PKESS OF VAN ANTWERP, BRAGG, f QJ 32. What cost 40 bundles of paper, containing 2 reams each, each ream weighing 60 pounds, at 8 cents 3 miTEr" per pound? 33. What cost 708 boxes of tomatoes, each containing 24 cans of 2 pounds each, at 11 cents a pound? 34. Find the cost of 82 boxes of calico, each box con- taining 40 bolts, and each bolt 30 yards, at $.066 per yard . 35. Find the amount received for 5 blocks of building lots, each block containing 12 lots, each lot being 25 feet front, the w^hole being sold at $8.75 per front foot. 36. What will be the wages of 240 men, employed 17 days, of 10 hours each, at 17 cents 5 mills per hour? ARTICLE 59. Division of United States Money. 1. Divide $49.50 cents by 33 cents. 2. Divide $393.75 by 75 cents. 3. Divide $200 by 32 cents. 4. Divide $333 by 45 cents. 5. Divide $1186.98 by $2.71. 6. Divide $3677.94 by $5 and 4 mills. 7. Divide $1608.88 by 33 cents 8 mills. 8. Divide $2162.45 by 30 cents 5 mills. 9. How much muslin, at 13 cents a yard, can be bought for $23.66? 10. How many sheep, at $3.75 apiece, can be bought for $600? 11. How many needles, at 3 mills apiece, can you buy for $19.38? 12. At $1.25 an acre, how much land can you buy for $995? 13. How many apples, at 1 cent 5 mills each, must be sold to realize $3? 40 RAY'S NEW TEST EXAMPLES. 14. How many planes, costing 85 cents each, can be bought for $129.20? 15. How many 20-cent tickets must be sold to make the receipts $500? 16. Divide $99.48 by 4. 17. Divide $95.004 by 7. 18. Divide $326.36 by 8. 19. Divide $436.032 by 9. 20. Divide $389 by 25. 21. Divide $440.44 by 77. 22. Divide $1500.496 by 491. 23. Divide $4226.427 by 603. 24. Nine horses cost me $1025.01; find the cost of each. 25. Sold 43 bushels of peaches for $120.40; how much was that per bushel? 26. $528.44 was divided equally among 11 heirs; find the share of each. 27. What must I charge per bushel for apples, so as to realize $526.50 for 2340 bushels? 28. 144 penknives cost $90; how much was that apiece ? 29. 900 pounds of cheese cost $49.50; how much did one pound cost? 30. 600000 pounds of cotton cost $45000; how much is that per pound? 31. If 40 horses cost $5318, what would 76 horses cost? 32. If 38 men earn $1136.20 in 26 days, what is each man's daily wages? 33. If grape settings sell at $3.50 per hundred, how much is that apiece? 34. What cost 750 pickles at $1.20 per hundred? 35. If 16 chests of tea sell for $460.80, at 60 cents a pound, how many pounds in each chest? PKOMISCUOUS EXAMPLES. 41 ARTICLE 60. Promiscuous Examples. 1. Paid for land, $970.50; for buildings, $1963.60; for horses, $180.75; for cattle, $217.50; for seeds, $29.50; for tools, $36.40; for harness, $82.50; for provisions, $200; and for hogs, $319.25. Find the total expenditure. 2. What cost 5 sofas, at $13.75 each, and 7 lounges, at $4.60 each? 3. Gave $108 for 45 yards of cloth, which I sold for $116.10; find my gain per yard. 4. A dealer bought peaches at $2.50 a bushel ; how many bushels must he sell, at a profit of 70 cents a bushel, to receive $144? 5. What cost 1750 picture cards at $1.40 a hundred? 6. I saved $104.52 in 6 months; if my salary was $80 a month, what were my expenditures each month? 7. I saved $130.56 in 8 months; if my expenses were $80 a month, what was my monthly salary? 8. What cost 3700 papers at $2.20 a hundred? 9. A company owes $120000, and its assets amount to $30780; the deficit is collected from 15000 shares of stock. How much is that on each share? 10. How much will be left from a hundred dollar bill after spending the following amounts: $3.60, $11.17, 50 cents, $1.96, $6.40, $8.33, $29.08. and 98 cents. 11. A contractor agrees to grade a road for $14000; he pays a foreman $5 a day, for 80 days; 25 cart drivers $2.25 a day, for 75 days; and 83 laborers $1.30 a day for 77 days. Find his profit. 12. Sold 29 horses for $1914, losing $159.50; what did each cost? 13. Sold a farm of 46 acres for $3000, gaining $7.10 per acre; what did the farm cost? 42 KAY'S NEW TEST EXAMPLES. 14. What will I save in 14 months, if I earn $75 each month, and spend $39.25 per month? 15. I worked 13 weeks at $13.75 per week, and saved $58.50 during that time; what were my weekly ex- penses? 16. How many dimes in $40? 17. How many half-eagles in $1080? 18. How many 3-cent pieces should be given for 240 eagles? 19. How many 5-cent pieces should be given for 720 quarter-eagles ? 20. If a man had one of each of the gold coins, how many quarter-dollars could he get for them? 21. Invested $4329 in cattle at $18.50 a head, and sold them at $23.08 a head; what was my gain? 22. Bought a house for $3300 ; made some repairs, and sold it for $4250, gaining $487.75. What was the cost of the repairs? 23. How many days, of 11 hours each, must a man work to earn $499.07, at 13 cents an hour? 24. Bought 40600 pounds of sugar for $2639, and sold it at a gain of 5 mills per pound; what was my gain? 25. Bought 15600 pounds of coffee for $5850, and sold it for $6162; how much was my gain per pound? 26. Bought rice for $3573 ; sold it for 5 cents per pound, gaining 5 mills per pound; how many pounds did I buy? 27. What cost 2468 pounds of butter, on which $86.38 was gained by selling it at 30 cents a pound? 23. Forty barrels of coal oil were bought for $241; how much was gained by selling at 15 cents a gallon, there being 50 gallons in each barrel? 29. Fifty barrels of molasses cost $1152, at 48 cents a gallon; how many gallons in each barrel? UNITED STATES MONEY. 43 30. A team pays $1.75 for toll, at the rate of 25 cents for 10 miles; how far does it go? 31. The expenses of a church festival were $237.52, and the gain was $701.98; how many 25-cent tickets had been sold? 32. A worked 47 days, at $2.55 per day; B worked 4 days longer than A, but received only the .same amount. How much did B earn per day? 33. Find the cost of 40 boxes, each containing 24 cans, and each can holding 6 pounds of canned peaches, boxes costing 25 cents each, cans 5 cents each, and peaches 4 cents per pound. Find the amount of the following bills : 34. 35 yards Muslin, at $0,12 per yard. 47 do Calico, u .08 do. 23 do Delaine, a .16 do. 13 do Alpaca, a .35 do. 21 do Silk, a 1.05 do. 10 do Satin, a 1.25 do. 7 do Velvet, a 2.40 do. 35. 4 pounds Tea, at $1.15 per pound. 7 do Coffee, u .32 do. 15 do Sugar, tt .13 do. 20 do Beef, tt .09 do. 17 do Ham, a .12 do. 12 do Cheese, a .15 do. 19 do Starch, a .09 do. 36. 400 feet Pine, at $0.025 per foot. 720 do Poplar, a .03 do. 560 do Walnut, a .07 do. 875 do Oak, a .02 do. 94 do Beech, tt .045 do. 120 do Cedar, n .06 do. 44 RAY'S NEW TEST EXAMPLES. REDUCTION. ARTICLE 63. Dry Measure. 1. Reduce 4 bu. 3 pk. 2 qt. 1 pt. to pints. 2. Eeduee 9 bu. 2 qt. 1 pt. to pints. 3. Eeduee 18 bu. 3 pk. 1 pt, to pints. 4. Reduee 36 bu. 3 qt. to pints. 5. Reduee 89 bu. 2 pk. to quarts. 6. Reduee 4789 pt. to bushels. 7. Reduee 5766 qt. to bushels. 8. Reduce 99 bu. 3 pk. 7 qt, 1 pt. to pints. 9. Reduce 583 bu. 1 pt. to pints. 10. Reduce 123456 pt. to bushels. 11. Reduce 4933 pk. to pints. 12. Reduce 25616 bu. to pints. 13. Reduce 25616 pt. to bushels. 14. Reduce 12345 qt. to pecks. 15. Reduce 7 million bushels to quarts. ARTICLE 64. Liquid Measure. 1. Reduce 38 gal. 3 qt. to pints. 2. Reduce 1025 gi. to gallons. 3. Reduce 87634 gal. to pints. 4. Reduce 93 gal. 2 qt. 1 pt, to gills. 5. Reduce 23867 pt. to gallons. 6. Reduce 8642 gal. to gills. 7. Reduce 99 gal. 3 qt. 2 gi. to gills. 8. Reduce 3732 gills to quarts. 9. Reduce 73 gal. 3 qt. 1 pt. 1 gi. to gills. 10. How many gallons in 33033 cubic inches? 11. How many cubic inches in 500 gallons? 12. A vessel measures 52206 cubic inches; how many gallons would it hold? KEDUCTION. 45 ARTICLE 65. Avoirdupois Weight. 1. Eeduce 3 T. to pounds. 2. Eeduce 5 T. 13 cwt. to pounds. 3. Eeduce 9 T. 1 cwt. 50 Ib. to pounds. 4. Eeduce 7 T. 19 cwt. 99 Ib. to pounds. 5. Eeduce 13 T. 13 Ib. to pounds. 6. Eeduce 4 T. 17 cwt. to ounces. 7. Eeduce 3 T. 20 Ib. 5 oz. to ounces. 8. Eeduce 12945 Ib. to tons. 9. Eeduce 98400 Ib. to tons. 10. Eeduce 876543 Ib. to tons. 11. Eeduce 38742 T. to ounces. 12. Eeduce 160080 oz. to tons. 13. Eeduce 71 T. 17 cwt. 71 Ib. to pounds. 14. Eeduce 711771 Ib. to tons. 15. Eeduce 40000000 oz. to tons. 16. Find the weight of 375 balls weighing 32 pounds each. 17. Find the weight of 3000000 candles weighing 3 ounces each. 18. Find the weight of 3456 20-pound cannon balls. 19. Eeduce 15999999 oz. to tons. 20. What is the weight of 357 boxes of alum, weigh- ing 56 pounds each? ARTICLE 66. Long Measure. 1. Eeduce 49 yd. 2 ft. 9 in. to inches. 2. Eeduce 53 yd. 7 in. to inches. 3. Eeduce 41 mi. 200 rd. to rods. 4. Eeduce 77 yd. 2 ft. to inches. 5. Eeduce 4953 mi. to rods. 6. Eeduce 5678 in. to yards. 46 KAY'S NEW TEST EXAMPLES. 7. Eeduce 38257 rd. to miles. 8. Eeduce 498 yd. 11 in. to inches. 9. Eeduce 373845 rd. to miles. 10. Eeduce 39G01 in. to yards. 11. Eeduce 39601 mi. to rods. 12. Eeduce 39601 rd. to miles. ARTICLE 67. Square Measure. 1. Eeduce 7 A. 100 sq. rd. to square rods. 2, Eeduce 3 sq. mi. 300 A. to square rods. 3. Eeduce 19 sq. mi. 19 A. 19 sq.rd. to square rods. 4, Eeduce 18 sq. yd. 8 sq. ft. 118 sq. in. to square inches. 5. Eeduce 39 sq. mi. 90 sq. rd. to square rods. 6, Eeduce 99 sq. yd. 99 sq. in. to square inches. 7, Eeduce 50000000 sq. mi. to square rods. 8. Eeduce 1 billion square inches to square yards. ARTICLES 68 AND 69. Rectangles. Find the area of the following : 1. A floor 18 ft. long and 15 ft. wide. 2. A carpet 27 ft. long and 22 ft. wide. 3. A platform 80 ft. long and 16 ft. wide. 4. A pavement 40 ft. long and 9 feet wide. 5. A ceiling 36 ft. long and 20 ft. wide. 6. A lot 72 rd. long and 60 rd. wide. 7. A farm 80 rd. long and 76 rd. wide. 8. A field 100 rods square. Find the cost of the following : 9. The carpet in example 2 at $1.30 a sq. yd. 10. The pavement in example 4 at 30 cents a sq. yd. 11. The farm in example 7 at $17.75 per A. 12. The platform in example 3 at 3 cents per sq. ft. KEDUCTION. 47 13. A farm extends along the road 60 rods ; how wide must it be to contain 45 A.? 14. A road is 3 rods wide; how long must it be to contain 120 A.? 15. A farm is 100 rods long and 96 rods wide; how much wheat will it produce at the rate of 13 bushels to the acre? 16. A roof 100 feet long requires 300 square yards of roofing; how wide is it? 17. A floor is 40 feet long and requires 120 square yards of carpet; how wide is it? ARTICLE 70. Solid or Cubic Measure. 1. Eeduce 3483648 cu. in. to cubic yards. 2. Reduce 3 cu. yd. 300 cu. in. to cubic inches. 3. Eeduce 746496 cu. in. to cubic yards. 4. Eeduce 9856 cu. ft. to cords. 5. Eeduce 11 C. Ill cu. ft. 1111 cu. in. to cubic inches. 6. How many cubic yards in a cellar 40 feet long, 18 feet wide, and 9 feet deep? 7. How many cords in a wood-pile 120 feet long, 8 feet high, and 4 feet wide? 8. How many cubic yards of masonry in a stone pier 320 feet long, 36 feet wide, and 12 feet thick? 9. What will be the cost of a breakwater 900 feet long, 6 feet thick, and 12 feet high, at $2.75 per cubic yard ? 10. Find the cost of a pile of wood 40 feet long, 40 feet wide, and 8 feet high, at $3.75 a cord. 11. How many inch cubes of lead can be cast from a mass 3 feet long, 1 foot high, and 2 feet wide? 12. Find the cost of digging a ditch 12 feet wide, 6 feet deep, and 285 feet long, at $.75 a cubic yard. 48 KAY'S NEW TEST EXAMPLES. ARTICLE 71. Time Measure. 1. Eeduce 3 da. 2 hr. 30 min. to seconds. 2. Eeduce 11 weeks to minutes. 3. Eeduce 3 wk. 3 da. 3 hr. 3 min. 3 sec. to seconds. 4. Eeduce 9 wk. 9 hr. to seconds. 5. Eeduce 43 da. 43 sec. to seconds. 6. Eeduce 777600 sec. to weeks. 7. Eeduce 45678 min. to days. 8. Eeduce 87500 days to seconds. 9. Eeduce 72000 min. to weeks. 10. How many minutes in the year 1890? 11. How many minutes in the last three months of the year? 12. How many seconds in February, 1889? 13. How many seconds in 5 leap years? 14. Eeduce 3 common years to hours. 15. A clock ticks 120 times in a minute; how many ticks will it make in the year 1892? 16. Eeduce 19 wk. 5 da. 21 hr. 20 min. to minutes. ARTICLE 73. Miscellaneous Tables. 1. Eeduce 17 Ib. 10 oz. 16 pwt. to grains. 2. Eeduce 18 Ib. 18 gr. to grains. 3. Eeduce 24 Ib. 11 oz. 19 pwt, 23 gr. to grains, 4. Eeduce 87340 gr. to pounds. 5. Eeduce 50660 pwt. to pounds. 9 6. Eeduce 31275 Ib. to pennyweights. 7. Eeduce 15 thousand gr. to pounds. 8. Eeduce 4 Ib. 4 oz. 4 gr. to grains. 9. Eeduce 10 Ib. 10 pwt. to grains. 10. Eeduce 3 Ib 9 3 3 1 9 14 gr. to grains. 11. Eeduce 9 Ib 3 3 2 9 to scruples. REDUCTION. 49 12. Eeduce 14 Ib 7 g 7 gr. to grains. 13. Eeduce 45677 gr. to pounds. 14. Eeduce 3478 3 to pounds. 15. Eeduce 12345 9 to pounds. 16. Eeduce 7 Cong, to f. g. 17. Eeduce 3 O. 2 f. g to minims. , 18. Eeduce 71 Cong. 3 f. 3 to f. 3. 19. Eeduce 4 ft. 6 in. to lines. 20. Eeduce 5 feet to hands. 21. Eeduce 17 leagues to miles. 22. Eeduce 16 spans to yards. 23. In 17 hands how many feet? 24. In 20 yards how many spans? 25. Eeduce 52 spans to hands. 26. Eeduce 80 paces to fathoms. 27. Eeduce 75 hands to fathoms. 28. Eeduce 25 chains to rods. 29. Eeduce 37, 37', 37" to seconds. 30. Eeduce 19, 19" to seconds. 31. Eeduce 37864" to degrees. 32. Eeduce 450 to seconds. 33. How many things in 30 dozen? 34. How many things in 15 gross? 35. How many things in 5 great gross? 36. Eeduce 15 score to dozens. 37. Eeduce 360 score to gross. 38. What cost 12 kegs of nails at 6 cents a pound? 39. What cost 12 barrels of flour at 3 cents a pound ? 40. What cost 12 barrels of pork at 8 cents a pound? 41. What cost 12 casks of lime, at 6 mills per pound? 42. What cost 1872 rings at 80 cents a gross? 43. What cost 7 great gross of needles, at 3 cents a dozen? 44. What cost 7 great gross of pins at 3 cents a gross? R. T. E. 4. 50 KAY'S NEW TEST EXAMPLES. 45. What cost 9 gross of braces, at 7 cents apiece? 46. What cost 18 quires of drawing paper at 4 cents a sheet? 47. How many sheets of paper in 6 bundles? 48. A ream of paper will make how many 8vo. leaves? 49. Three reams of paper will make how many 12 mo. pages? 50. How many reams of paper will be required for 3000 octavo books of 320 pages each? ARTICLE 74. PromiscMous Examples. 1. Eeduce 49 yd. 2 ft. to inches. 2. Eeduce 7 Ib. 3 pwt. to grains. 3. Eeduce 174528 sq. in. to square yards. 4. Eeduce 12500" to degrees. 5. Eeduce 504000 cu. in. to cubic yards. 6. Eeduce 3 Ib 7 3 2 9 to grains. 7. Eeduce 863990 sec. to weeks. 8. Eeduce 3329 pt. to bushels. 9. Eeduce 14 great gross to dozens. 10. Eeduce 7 T. 13 cwt. to pounds. 11. Eeduce 3734 in. to yards. 12. Eeduce 15 cords to cubic inches. 13. Eeduce 5678 pt. to gallons. 14. Eeduce 1016064 Ib. flour to barrels. 15. Eeduce 5400 scores to gross. 16. Eeduce 3456 bu. to quarts. 17. Eeduce 39750 pwt. to pounds. 18. Eeduce 14 T. 14 Ib. to ounces. 19. Eeduce 23 gallons to f. 3. 20. Eeduce 333360 min. to weeks. 21. Eeduce 7599 pt. to gallons. 22. Eeduce 435670 sq. rd. to square miles. REDUCTION. 51 23. Keduce 240 mi. to rods. 24. Eeduce 78 gal. 3 qt. 1 pi. to pints. 25. Eeduce 19 wk. 20 sec. to seconds. 26. Eeduce 310 mi. 310 rd. to rods. 27. Eeduce 49600 oz. to T. 28. Eeduce one million sec. to weeks. 29. Eeduce 384 cu. yd. to cords. 30. Eeduce 5350 Ib. to grains. 31. Eeduce 12345 qt. to bushels. 32. Eeduce 13 common years to minutes. 33. Eeduce 12 cu. yd. 23 cu. ft. to cubic inches. 34. Eeduce 39 T. 39 Ib. to pounds. 35. Eeduce 8 Ib 8 8 gr. to grains. 36. Eeduce 46 sq. yd. 2 sq. ft. 36 sq. in. to sq. in. 37. Eeduce 9876 pt. to gallons. 38. Eeduce 10000 in. to yards. 39. Eeduce 1284 pt. to bushels. 40. Eeduce 11 7 3 2 9 to grains. 41. Eeduce 5 sq. mi. 5 sq. rd. to square rods. 42. Eeduce 162 C. to cubic yards. 43. Eeduce 26 reams to 16 mo. leaves. 44. Eeduce 47580" to degrees. 45. Eeduce one million pt. .to gallons. 46. Eeduce 3500 gr. to g. 47. Eeduce 6399 pt. to bushels. 48. Eeduce 24 reams to sheets. 49. Eeduce 793863 sq. in. to square yards. 50. Eeduce one million oz. to tons. 51. Eeduce 79 yd. 11 in. to inches. 52. Eeduce 19 C. 1600 cu. in. to cubic inches. 53. Eeduce 704000 sq. rd. to square miles. 54. Eeduce 137 bu. 3 pk. to pints. *55. Eeduce 5 wk. 5 da. 15 hr. 55 sec. to seconds. 56. Eeduce 13 mi. 130 rd. to rods. 52 KAY'S NEW TEST EXAMPLES. 57. Reduce 1600 barrels of pork to pounds. 58. Eeduce 30 T. 1 cwt. to ounces. 59. Reduce 217728 cu. in. to cubic yards. 60. Reduce 6920 pt. to gallons. 61. Reduce 10 great gross to scores. 62. Reduce 456789 oz. to tons. 63. Reduce ten thousand pt. to bushels. 64. Reduce 14 23" to seconds. 65. Reduce 4720 qt. to gallons. 66. Reduce one million sq. in. to square yards. 67. Reduce 6732 in. to yards. 68. Reduce 5280 minims to f. 3. 69. Reduce 565 bu. 1 pt. to pints. 70. Reduce 3456000 sec. to weeks. 71. Reduce 3456000 12mo. pages to reams. 72. Reduce 288000 oz. to tons. 73. Reduce 387 A. 100 sq. rd. to square rods. 74. Reduce 17 leagues to rods. 75. Reduce 87 cu. yd. 25 cu. ft. to cords. 76. What cost 35 bushels of apples at 18 cents a peck? 77. What cost 13 bushels of salt at 3 cents a pint? 78. How much iron will be required to make 1000 4-oz. spikes? 79. How much wine will be needed to fill 80 dozen pint bottles ? 80. A man's expenses are $1.17 a day; how much is that for July? 81. How many rings, weighing 6 pwt. each, can be jnade from 3 Ib. of gold? 82. 414 gallons of brandy were put in bottles contain- ing 3 gills each; how many dozen bottles were required? 83. Find the cost of a pile of wood 40 feet long, 8 feet wide, and 8 feet high, at $3.75 per cord. fi4 What cost 20 bushels of apples at 20 cents a peck? REDUCTION. 53 85. A lawn 120 feet long, and 54 feet wide, was sodded at a cost of 19 cents per square yard; what was the total cost? 86. 561 pounds of iron were made into horse-shoes weighing 6 ounces each; how many were made? 87. How many 3-grain pills can be made from 5 of quinine? 88. If sound moves 1124 feet per second, how long will it be in passing over 39340 yards? 89. How many bottles, holding 1 pt. 3 gi. each, can be filled from 168 gallons? 90. A comet moves 40" per day; how far will it move in 120 days? 91. What cost a carpet 21 feet long and 15 feet wide, at $1.75 per square yard? 92. How many pounds in 480 dozen boxes of baking powder holding 15 ounces each? 93. How much silver will be required to make 10 dozen spoons, each weighing 15 pwt.? 94. How many cords of wood can be cut on 25 acres, at the rate of 72 cubic feet to a square rod? 95. If bottles hold 1 pt. 2 gi. each, how many dozen bottles can be filled from 126 gallons? 96. How many sashes, each 3 yd. 1 ft. long, can be cut from 200 yards of silk? 97. 500 bushels of peaches were packed in baskets, each holding 3 pk. 1 qt. ; how many baskets were re- quired? 98. A paper containing 2 5 1 9 of medicine was divided into pills weighing 5 grains each, which were sold at 2 cents apiece; how much was received for it? 99. If 25 sq. rd. produce 1 bushel of wheat, how many bushels can be raised on a square mile ? 54 RAY'S NEW TEST EXAMPLES. 100. If a weaver can weave 10 sq. ft. of carpet in an hour, bow many sq. yd. can he weave in 15 days, work- ing 12 hours per day? 101. How many plates, each weighing 2 Ib. 8 oz., would be required to weigh 7 tons? 102. What cost 3 Ib. 4 oz. of gold plate, at $.95 per pwt. ? 103. Three cwt. of indigo was put up in ounce papers; how many dozen papers would that give? 104. A cistern containing 3003 gallons is emptied by a pipe carrying 1 gal. 1 gi. per minute; how long will it take to empty it? 105. A boy walks a rod in 3 seconds; how long will he be in walking 15 miles? 106. At 5 cents a pint, how many bushels of straw- berries can be bought for $20? 107. A publisher issued an edition of 5000 12mo. books of 288 pages each ; how many reams of paper were re- quired ? 108. If a pint of water weigh one pound, how many gallons will be required to make a weight of 8 tons? 109. What cost 13 yards of antique lace, at $20 per inch? 110. What sum will be received for 57 bushels of apples, at 24 cents per peck? 111. What will be the cost of fencing a field 180 rods long and 56 rods wide, at 75 cents per rod? 112. Three ounces and two drams of medicine was di- vided into powders weighing 13 grains each; how much would be received for the powders, at 15 cents apiece? 113. Fifteen bushels of cherries cost $33.60; how much is that per pint? 114. How much will a man earn in 9 weeks, at $2.25 per day? REDUCTION. 55 115. A ship sails 10' 30" per hour; how many days will it take to sail 28? 116. What will wine cost, to fill 40 dozen bottles, hold- ing 3 gills each, at $2.50 a gallon? 117. A block of stone is 8 ft. long, 8 ft. wide, and 8 ft. thick ; how much will it weigh if a cu. ft. weighs 625 Ibs? 118. Find the cost of 300 bushels of oysters, at 12 cents per peck. 119. If a railway train can go 22 miles 160 rods in 1 hour, how long will it require to go 1710 miles? 120. What cost 9 tons of hay, at 9 mills per pound? 121. A tank will hold 1000 gallons of water ; how many cubic feet in it? 122. A steel plate is 2 feet long and 16 inches wide, and weighs 2 ounces to each square inch ; what is it worth, at $0.075 per pound? 123. A man's income being $1.33 every hour, what will it be in the year 1895? 124. What cost 375 fathom of rope, weighing 2 pounds per foot, at 5 cents 5 mills per pound? 125. How many score in 30 great gross? 126. Sold berries at 6 cents a pint, and realized $15.12 ; how many bushels were sold? 127. What cost 400 gallons of molasses, at 7 ct. a pint? 128. How many rings, weighing 6 ounces each, can be made from 141 pounds of iron? 129. How many plates, weighing 6 ounces each, can be made from 141 pounds of silver? 130. Wheat weighs 60 pounds per bushel ; find the cost of 30720 pounds, at 90 cents a bushel. 131. What will be the cost of paving a street 2700 feet long, and 40 feet wide, at $0.72 per square yard? 132. If a machine will peg a shoe in 4 minutes, how many dozen will it peg in 6 daystof 10 hours each? 56 KAY'S NEW TEST EXAMPLES. 133. A cistern containing 480 gallons of water has two leaks: from one, 3 gills run out per minute; from the other, 13 gallons per hour. How much w T ill be left in the cistern at the end of 8 hours? 134. 550 bushels of corn were bought at 44 cents a bushel, and retailed at 14 cents a peck; how much was gained ? 135. How long would it take a tortoise to crawl a league, moving 4 rods an hour and 15 hours a day? 136. A man eats 2 Ib. 3 oz. daily; how many weeks would 2 T. 9 cwt, last him? 137. A had 150 barrels of flour ; B had the same weight of beef; how many barrels would it fill? 138. How many bags, of 2 bu. 2 qt. each, will be re- quired to contain 2145 bushels of wheat? 139. How long would it take to build a road 8G mi. 20 rd. long, if 1 mi. 20 rd. can be made in a day? 140. What cost 256 cubic yards of wood, at $3. 1 7 a cord? 141. If 3 bu. 2 pk. of berries cost $8.40, how much is that per quart? 142. A man poured 48 gallons of wine into bottles con- taining 1 qt. 1 pt. each, and sold them at 60 cents per bottle ; how much did he receive? 143. How many gallons of essence will be required to fill 40 gross of bottles, each to contain 1 fluid ounce? 144. How many labels, 2 in. long and 1 in. wide, can be cut from 6 sheets of paper, each 4 ft. wide and 8 ft. long? 145. If 1 bu. 1 pk. of peaches cost $3, what will 1 bushel cost? 146. Twenty-four sheets were folded in 12mo. ; how many sheets would be required to make as many quarto leaves? COMPOUND NUMBEKS. 57 COMPOUND NUMBERS. ARTICLE 75. Addition of Compound Numbers. 1. Add together 4 bu. 2 pk. 5 qt. ; 17 bu. 3 pk. 1 qt. ; 9 bu. 2 pk. 6 qt. ; 16 bu. 3 pk. 5 qt. ; 5 bu. 1 pk. 3 qt; 2 bu. 7 qt. ; 1 pk. 2 qt. ; and 3 bu. 3 qt, 2. Add together 199 bu. 2 pk.; 83 bu. 3 pk. ; 65 bu. 1 pk.; 88 bu. 2 pk. ; 100 bu. 2 pk. ; 116 bu. 1 pk. ; 134 bu. 3 pk.; and 111 bu. 2 pk. 3. 27 gal. 3 qt. 1 pt, + 27 gal. 2 qt. 1 pt. 4- 27 gal. 1 qt. 1 pt. 4- 27 gal. 1 pt. + 27 gal. 3 qt. -f 27 gal. 2 qt. + 27 gal. 1 qt. = ? 4. 3 T. 17 cwt. 60 Ib. + 5 T. 15 cwt. 70 Ib. + 4 T. 90 lb. + 9 T. 19 cwt. 99 Ib. -f 7 T. 16 cwt. 4- 5 cwt. 92 lb.r=? 5. 15 gal. 1 pt, 4- 16 gal. 1 qt. 4- 17 gal. 1 qt. 1 pt. + 18 gal. 2 qt. + 19 gal. 1 pt. 4- 20 gal. 3 qt. 4- 21 gal. 1 pt. 4- 22 gal. 3 qt. 1 pt. = ? 6. Find the sum of 7 cwt, 29 lb. ; 9 cwt. 40 lb. ; 16 cwt, 67 lb. ; 13 cwt. 28 lb. ; 12 cwt. 71 lb. ; 10 cwt. 60 lb. ; 3 cwt. 33 lb.; and 16 cwt. 72 lb. 7. 29 gal. 2 qt. 1 pt, 4- 29 gal. 2 qt. 1 pt. 4- 29 gal. 2 qt. 1 pt, 4- 29 gal. 2 qt. 1 pt. 4- 29 gal. 2 qt, 1 pt. -f 29 gal. 2 qt, 1 pt, ==? 8. Find the sum of 7 yd. 2 ft. 11 in. ; 4 yd. 1 ft. 7 in.; 12 yd. 2 ft. 5 in.; 9 yd. 1 ft, 1 in. ; 12 yd. 1 in. ; 15 yd. 1 ft. 5 in. ; 6 yd. 7 in. ; and 10 yd. 1 ft. 11 in. 9. Add together 7 yd. 2 ft. ; 7 yd. 2 in. ; 6 yd. 1 ft. 7 in. ; 4 yd. 11 in. ; 9 yd. 2 ft. 6 in. ; 3 yd. 3 in. ; 12 yd. 2 ft. ; and 6 yd. 10 in. 10. 75 A. 4-*75 sq. rd. 4- 76 A. 76 sq. rd. 4- 77 A. 77 sq. rd. 4- 78 A. 78 sq. rd. 4- 72 A. 72 sq. rd. 4- 119 A. 140 sq. rd. == ? 58 BAY'S NEW TEST EXAMPLES. 11. 7 sq. yd. 7 sq. ft. 77 sq. in. + 8 sq. yd. 8 sq. ft. 88 sq. in. -f- 22 sq. yd. 22 sq. in. -f 49 sq. yd. 4 sq. ft. 48 sq. in + 39 sq. yd. 96 sq. in. == ? 12. Find the sum of 3 sq. mi. 300 A. ; 7 sq. mi. 500 A. ; 4 sq. mi. 444 A. ; 2 sq. mi. 222 A. ; 10 sq. mi. 229 A. ; and 5 sq. mi. 555 A. 13. 27 cu. yd. 26 cu. ft. -f 26 cu. yd. 25 cu. ft. + 25 cu. yd. 24 cu. ft. + 24 cu. yd. 23 cu. ft. + 23 cu. yd. 22 cu. ft. + 22 cu. yd. 21 cu. ft, = ? 14. 25 C. 17 cu. ft. + 25 C. 1700 cu. in. + 25 C. 117 cu. ft. 1170 cu. in. -f 252 C. 1717 cu. in. + 28 C. 127 cu. ft.+ 19 C. 127 cu. ft. 1727 cu. in. ==? 15. 3 da. 13 hr. 20 min. + 7 da. 17 hr. 27 min. -f- 3 da. 13 hr. 33 min. + 6 da. 23 hr. + 4 da. 6 hr. 56 min. + 11 da. 11 hr. 11 min. + 19 da, 19 hr. 59 min. =? 16. 5 da. 59 min. -|- 5 da. 58 min. + 5 da. 57 min. + 5 da. 56 min. -|- 5 da. 55 min. -f- 5 da. 54 min. -f- 5 da. 53 min. ? 17. 4 Ib. 9 oz. 12 pwt. + 6 Ib. 7 oz. 18 pwt. + 3 Ib. 10 oz. 10 pwt. + 5 Ib. 11 oz. + 2 Ib. 11 pwt. + 6 Ib. 6 oz. 16 pwt. + 13 Ib. 13 pwt, =:? 18. 2 5 2 9 10 gr. + 7 3 19 gr. + 5 3 1 9 16 gr. + 5 3 10 gr. + 2 3 2 9 1 gr. + 5 3 1 9 4 gr. == ? 19. 533329 + 432319 + 7529 + 7329 + 2543l9+3g5329+7 3 19+73l9=? 20. 4 score and 6 + 3 score and ten + 4 score and 8 + 4 score and 9 + 2 score and 18 + 3 score and 12 == ? 21. 14 35' 23" +17 49' 49" +26 30' 10" +30 59' 1" + 7 24' 48" + 13 29' 50" + 9 59" = ? 22. 8 15' 28" + 6 28' 29" + 7 30' 30" + 11 44' 32" +13 31' 31" +13 30' 31" = ? 23. 3 cong. 7 O. 11 f. + 5 corig. 4 O. 9 f . + 7 cong. 7 O. 7 f. % + 9 cong. 5 f. 3 + 7 cong. 7 O. + 5 O. 15 f. =? COMPOUND NUMBERS. 59 24. 2 f. g 4 f. 3 20 HL+ 3 f. g 5 3 40 rTt+ 7 f. 3 3 f. 3 40 nt+6 f. 2 f. 3 20 nt = ? 25. Seven barrels of whisky were guaged as follows: 49 gal. 3 qt. ; 51 gal. 2 qt. ; 48 gal. 3 qt. ; 55 gal. 2 qt. ; 52 gal. 2 qt. ; 53 gal. 1 qt.; and 50 gal. 2 qt. How much in all? 26. How much wood in 5 piles, containing respectively 25 C. 87 cu. ft,; 56 C. 112 cu. ft. ; 39 C. 41 cu. ft. ; 43 C. 16 cu. ft.; and 88 C. 88 cu. ft.? 27. Eggs were packed in 6 boxes : 29 doz. and 7 ; 40 doz. and 10 ; 35 doz. and 5 ; 60 doz. and 10 ; 38 doz. and 9 ; and 52 doz. and 7. How many dozen in all ? 28. Find the weight of 8 hogsheads of sugar, weighing as follows: 11 cwt. 83 Ib. ; 12 cwt. 46 Ib. ; 11 cwt. 55 Ib. ; 12 cwt, 19 Ib. ; 13 cwt, 1 Ib. ; 12 cwt. 52 Ib. ; 11 cwt. 93 Ib.; and 12 cwt, 51 Ib. 29. A farmer planted 17 A. 100 sq. rd. in wheat, 21 A. 120 sq. rd. in oats, 30 A. 50 sq. rd. in corn, 13 A. 60 sq. rd. in potatoes, 7 A. 40 sq. rd. in sorghum, and 11 A. 110 sq. rd. in broom-corn. How much land had he in cul- tivation? 30. A vessel sailed 13 da. 7 hr. to the first port, and stopped there 2 da. 20 hr ; then 25 da. 20 hr. to the second port, and stopped there 3 da. 23 hr. ; then 40 da. 5 hr. to the third port, and stopped there 2 da. 19 hr. ; then 60 da. 16 hr. to the starting point. How long was the voyage? 31. A railroad train traveled as follows: 14 mi. 125 rd. to first station; 9 mi. 77 rd. to second; 16 mi. 62 rd. to third; 31 mi. 35 rd. to fourth; 11 mi. 83 rd. to fifth; and then 18 mi. 98 rd. to its destination. What was the length of the trip? 32. Set down 3 da. 13 hr. 39 min. 26 sec, seven times, and then add them. 60 KAY'S NEW TEST EXAMPLES. ARTICLE 76. Subtraction of Compound Numbers. 1. From 40 bu. take 20 bu. 3 qt. 2. 39 bu. 1 pk. 1 qt. 19 bu. 3 pk. 3 qt. = ? 3. From 100 gal. take 49 gal. 3 qt, 2 gi. 4. From 353 gal. 1 pt. take 203 gal. 3 qt, 5. From 3 T. 13 cwt. 23 Ib. take 1 T. 18 cwt. 5 Ib. 6. From 1 T. 1 cwt. 1 Ib. 1 oz. take 11 cwt. 11 Ib. 11 oz. 7. From 47 mi. 180 rd. take 23 mi. 250 rd. 8. From 16 yd. 2 ft. 1 in. take 9 yd. 1 ft, 2 in. 9. 81 yd. 6 in. 18 yd. 8 in. = ? 10. From 9 sq. mi. 100' A. take 4 sq. mi. 370 A. 11. 39 sq. yd. 4 sq. ft. 44 sq. in. 21 sq. yd. 7 sq. ft. 89 sq. in. =? 12. From 300 sq. mi. 300 A. 100 sq. rd. take 100 sq. mi. 300 A. 150 sq. rd. 13. From 36 cu. yd. 10 cu. ft. 800 cu. in. take 8 cu. yd. 19 cu. ft. 900 cu. in. 14. Take 18 C. 1500 cu. in. from 81 C. 1478 cu. in. 15. 5 hr. 6 min. 22 sec. 2 hr. 20 min. 20 sec. = ? 16. From 7 wk. 6 da. 5 hr. 4 min. 3 sec. take 3 wk. 4 da. 5 hr. 6 min. 7 sec, 17. Take 9 Ib. 7 oz. 16 pwt. from 15 Ib. 3 oz. 3 pwt. 18. 5tb4g3 5 19 21b6g6329=_-? 19. From 14 7' 10" take 9 18' 30". 20. From 19 reams take 12 reams 4 quires. 21. From 3 gross 4 dozen take 1 gross 8 dozen. 22. From 1 O. 3 f. g 2 f . 3 take 13 f. . 23. If 25 bu. 3 pk. 2 qt. have be.en sold from 40 bu. of peanuts, what quantity is left? 24. A farmer has 450 bu. of potatoes; if he sells 273 bu. 2 pk. what quantity will he have left? COMPOUND NUMBERS. 61 25. The time between two cities by steamer is 2 wk. 2 hr. ; by railroad, 5 da. 19 hr. ; how much time is gained by the railroad route? 26. From a tank containing 327 gal. 2 qt. 1 pt., 10 gal. 3 qt. 1 pt. leaked out; how much remains? 27. If a tract of 36 A. 120 sq. rd. be cut from a farm of 120 A., how much will be left? 28. A quantity of pig iron, weighing 17 T. 5 cwt v 48 lb., was melted to make stove castings, which, when cast, weighed 17 T. 1 cwt. 90 lb. ; how much metal was lost in the work? 29. From a pile of wood containing 106 C. 105 cu. ft., there was taken away a boat load of 87 C. 120 cu. ft. ; how much remained? 30. A cart weighed 13 cwt. 80 lb., and, after being filled with coal, weighed 3 T. 11 cwt. 90 lb. ; what was the weight of the coal? 31. A ship was 13 7' 20" from a port, and sailed 4 43' 40" toward it; how far from the port was it then? 32. How much will be left of a mass of medicine weighing 1 lb 1 3., after 7 g 5 3 2 9 10 gr. have been made into pills? 33. A boat laden with 750 T. 60 lb. was sunk, and 473 T. 90 lb. of the freight was saved; how much was lost? 34. The regular time between two cities was 100 hr. 10 min., and the train arrived 3 hr. 52 min. ahead of time; how long had it taken to make the run? 35. A man contracted to deliver 100 C. of wood, and has only 78 C. 96 cu. ft.; how much does he lack? 36. A man having 89 bu. 1 pk. of clover seed, sold 37 bu. 3 pk. to each of his two brothers; how much has he remaining? 37. From 30 days subtract 5 da. 12 hr. 19 minutes three times. 62 KAY'S NEW TEST EXAMPLES. ARTICLE 77. Time between two dates. 1. Money was borrowed May 18, 1882, and returned Jan. 6, 1884; how long had it been kept? 2. The battle of Monmouth was fought June 28, 1778, and the battle of Antietam September 17, 1862; -what time elapsed between the two events? 3. Washington was born February 22, 1732, and died December 14, 1799; at what age did he die? 4. The pilgrims landed December 21, 1620; how long was that before the Declaration of Independence, July 4, 1776? 5. What time elapsed between the surrender at York- town, October 19, 1781, and the signing of the treaty of peace, September 3, 1783? 6. A child born December 3, 1876, commenced school August 27, 1883 ; at what age was that? 7. How old was Washington at the battle of Mon- mouth? (See examples 2 and 3.) 8. What time elapsed from the battle of Lexington, April 19, 1775, to the firing on Fort Sumter, April 12, 1861? ARTICLE 78. Time in days between two dates. 1. Find the number of days from Aug. 5 to the second day of the next December. 2. How many days from Nov. 15, 1871, to Jan. 18, 1872? 3. How many days from Oct. 20, 1877, to Mar. 15, 1878? 4. How many days from Jan. 12, 1880, to Oct. 15, 1880? 5. How many days from June 5 to Dec. 25? COMPOUND NUMBERS. 63 6. A servant was hired May 18, and discharged No- vember 29; for how many days should she be paid? 7. How many days from Apr. 6, 1875, to Apr. 1, 1876? 8. Corn was planted April 18, and was ripe Septem- ber 27; how many days was that? ARTICLE 79. Multiplication of Compound Numbers. 1. 3 bu. 2 pk. 5 qt. 1 pt. X 8 = ? 2. 7 gal. 3 qt. 1 pt. 3 gi. X 8 = ? 3. 3 cwt. 27 Ib. 8 oz. X 10 = ? 4. 5 yd. 2 ft. 7 in. X H -=? 5. 3 sq. yd. 7 sq. ft. 72 sq. in. X 6=? 6. 7 cu. ft. 700 cu. in. X 10=? 7. 3 oz. 7 pwt. 10 gr. X 24 = ? 8. 3 3 2 9 12 gr. X 60=? 9. 3 gal. 1 pt. 1 gi. X?2=? 10. 2 10' 20" X 36=? 11. 3 quires 10 sheets X 120=? 12. 3 mi. 190 rd. X?7=? 13. 13 hr. 24 min. 36 sec. X 99 = ? 14. What will be the weight of 27 castings, 1 T. 12 cwt, 42 Ib. each? 15. If an acre will produce 6 bu. 3 pk. 5 qt. of wheat, how much can be raised on 20 acres? 16. If a stream flows 17 yd. 2 ft. 8 in. in a minute, how far would that be in an hour? 17. If a square rod produces 7 qt. 1 pt. of straw- berries, what quantity could be raised on 1 A.? 18. A steamer makes a trip in 1 da. 5 hr. 19 min.; what time would be required for 20 trips? 19. If a quart of berries can be picked in 14 min. 20 sec., how long would it take to pick 1 pk. ? 64 KAY'S NEW TEST EXAMPLES. 20. If a herd of cattle consumes 9 T. 3 cwt. 18 Ib. daily, how much fodder would be required for the month of November? 21. If 34 sq. yd. 8 sq. ft. 60 sq. in. of flooring are re- quired for one floor, how much will be needed for 14 floors ? 22. If 1 qt. of seed will produce 1 bu. 1 pk. 1 qt. of grain, how much grain will 1 bu. of seed produce? ARTICLE 80. Division of Compound Numbers. 1. Divide 32 bu. 1 pk. 3 qt. by 9. 2. Divide 1 T. 9 cwt. 80 Ib. 8 oz. by 8. 3. Divide 22 yd. 2 ft. by 6. 4. Divide 8 sq. yd. 4 sq. ft. 16 sq. in. by 10. 5. Divide 2 da. 15 hr. 12 min. by 18. 6. Divide 3 oz. 11 pwt. 16 gr. by 20. 7. Divide 2 6 3 by 12. 8. Divide 225 gal. 3 qt. 1 pt. 2 gi. by 30. 9. Divide 238 yd. 1 ft. by 33. 10. Divide 67 sq. yd. by 54. 11. Divide 230 da. 13 hr. 20 min. by 100. 12. Divide 19 cu. yd. 9 cu. ft. 864 cu. in. by 19. 13. A man raised 237 bu. 3 pk. 2 qt. of raspberries on 10 A. ; how much was that per acre? 14. If 19 jars would contain 103 gal. 3 qt. 1 pt. 1 gi., what would one contain? 15. If 11 cwt. 79 Ib. 12 oz. of sugar be packed in 12 kefirs, how much will each contain? O " ' 16. One hundred cu. yd. of earth are to be hauled away in 18 carts; how much will that be for each? 17. A glacier moved 43 yd. in 701 da. 13 hr. 22 min.; how long did it take to move 1 yd.? LONGITUDE AND TIME. 65 18. A planet moved 13 30' -50" in 25 days; what would be the average motion per day? 19. Fifteen equal bins contain 3740 bu. 2 pk. 4 qt. of wheat; how much is in each? 20. A steamer goes 183 mi. 144 rd. per day; how far is that per hour? 21. In 7 days, of 10 hours each, a furnace will turn out 242 T. 18 cwt. of blooms; how much is that per hour? 22. A gardener raised 275 bu. of beets on an acre of ground ; what was the yield per square rod ? LONGITUDE AND TIME. ARTICLES 81 AND 82. Find the differences in time, corresponding to the following differences in longitude: 1. 40. 2. 33 20'. 3. 36 17'. 4. 69 51'. 5. 100 10'. 6. 49 13' 30". 7, 66 45". 8. 70 17' 15". 9. 99 9'. 10. 111 51' 30". 11. 58 58' 15". 12. 97 53'. Find the differences in longitude, corresponding to the fol- lowing differences of time: 13. 11 hr. 17 min. 13 sec. 14. 6 hr. 59 min. 17 sec. 15. 10 hr. 10 min. 10 sec. 16. 7 hr. 17 min. 27 sec. 17. 15 hr. 14 min. 29 sec. 18. 4 hr. 45 min. 10 sec. 19. 5 hr. 29 min. 25 sec. 20. 47 min. 47 sec. 21. A man travels east 29; will his watch be fast or slow then, and how much? 22. A boat sails 47 west ; how much will her chro- nometer gain or lose on the time at the point reached t R. T. E. 5. 66 KAY'S NEW TEST EXAMPLES. 23. A team travels eastward 45' a day; will its day be lengthened or shortened, and how much? 24. What is the difference of time between two places whose longitudes are 29 east, and 54 west? 25. When it is 7 o'clock A. M. at a place in 93 west longitude, what is the time at another place in 39 west longitude? 26. When it is 7 o'clock A. M. at a place in 107 east longitude, what is the time at another place in 40 east longitude? 27. When it is 11 o'clock A. M. at a place in 40 west longitude, what is the time at another place in 70 east longitude ? 28. When it is 3 o'clock P. M. at a place in 3 east longitude, what is the time at another place in 68 west longitude? 29. When it is 6 o'clock A. M. in 90 east longitude, what is the time in 90 west longitude? 30. What is the difference of time between two places, one in 37 35' east longitude, the other in 47 10' west longitude? FA CTORING. ARTICLE 87. Find the Prime Factors: 1. Of 51. 8. Of 120. 15. Of 252. 2. Of 52. 9. Of 132. 16. Of 561. 3. Of 62. 10. Of 168. 17. Of 882. 4. Of 63. 11. Of 196. 18. Of 828. 5. Of 72. 12. Of 198. 19. Of 2662. 6. Of 75. 13. Of 204. 20. Of 3087. 7. Of 76. 14. Of 207. 21. Of 4356. FACTORING. 67 What Prime . Factors 1. 60 and 80? 2. 90 and 120? 3. 80 and 120? 4. 135 and 180? 5. 126 and 210? 6. 324 and 432? 7. 324 and 594? 8. 264 and 638? 9. 462 and 819? 10. 385 and 595? 11. 363 and 1419? ARTICLE 88. are common to : 12. 48, 72, and 84? 13. 78, 104, and 143? 14. 192, 252, and 348? 15. 64, 104, 144, and 376? 16. 135, 180,210,and375? 17. 144, 168, 192, and 240? 18. 117, 143, 286, and 390? 19. 126, 196, 238, and 266? 20. 187, 231, 275, and 308? .21. 147, 210, 315, and 364? 22. 384, 486, 324, and 510? ARTICLE 89. Greatest Common Divisor. Find the Greatest Common 1. Of 48 and 84. 2. Of 40, 60, and 90. 3. Of 117 and 171. 4. Of 889 and 560. 5. Of 124 and 600. 6. Of 390 and 702. 7. Of 392 and 637. 8. Of 770 and 891. 9. Of 873 and 378. 10. Of 656 and 1066. 11. Of 980 and 2401. 12. Of 3003 and 21000. 13. Of 1008 and 1584. 14. Of 1296 and 2304. 15. Of 16983 and 18574. 16. Of 243, 324, and 432. Divisor : 17. Of 56, 84, and 126. 18. Of 80, 120, and 180. 19. Of 468, 648, and 864. 20. Of 675, 945, and 1053. 21. Of 980, 2002, and 15001. 22. Of 289, 391, and 493. 23. Of 288, 387, and 486. 24. Of 3375, 8205, and 15000. 25. Of 81, 135, 450, and ' 780. 26. Of 63, 144, 216, and 297. 27. Of 1120, 960, 888, and 666. 68 RAY'S NEW TEST EXAMPLES. ARTICLE 90. Least Common Multiple. Find the Least Common Multiple : 1. Of 8, 12, 16, and 20. 2. Of 9, 12, 16, and 20. 3. Of 12, 16, 20, and 24. 4. Of 16, 20, 25, and 40. 5. Of 36, 42, 48, and 54. 6. Of 24, 30, 42, and 28. 7. Of 60, 66, 30, and 36. 8. Of 21, 35, 55, and 84. 9. Of 16, 18, 20, and 22. 10. Of 16, 18, 20, and 30. 11. Of 12. Of 18, 20, 24, and 36. 13. Of 24, 54, 84, and 144. 14. Of 121 and 122. 15. Of 221 and 323. 16. Of 169 and 325. 17. Of 343 and T35. 18. Of 150, 225, and 375. 19. Of 100, 200, and 300. 20. Of 14, 24, 44, and 42. 21. Of 143 ami; 175. 22. Of 143 and 176. 16, 18, 20, and 24. 23. Of 12, 16, 24, 36, and 72. 24. Of 30, 36^48, 64, and 80. 25. Of 18, 26, 54, and 78. 26. Of 576,^84, 288, 768, and 256. 27. Of 8, 9, 10, 11, a*id 12. 28. Of 45, 75, 81, 72, and 54. 29. Of 245, 343* 441, and 98. 30. Of 123, 205 ; 287, and 246. ARTiLE*,91. Cancellation. 1. How often is 12 Contained in 4 times 27? 2. Divide 18 X 21 by 14 X 9. 3. In 16 times 18 how many times 12? 4. How often is 6 X 8 contained in 16 X 18? 5. How many score in 12 X 25? 6. How many flower-beds 4 feet long and 3 feet wide, can be made from a plat 36 feet long and 18 feet wide? 7. Divide 8 X 9 X 10 X 12 by 3 x * X 5 X 6- FRACTIONS. 69 8. Sold six dozen tumblers at 8 cents apiece, and spent the money for yarn at 18 cents a pound; Low many pounds did I receive? 9. How many barrels of sugar, at $15 a barrel, will pay for 18 hogs, at $20 apiece? 10. DLvide 18 X 20 X 24 X 32 by 27 X 16 X 40. 11. How many lots 5 feet square can be cut from a lot 30 feet square? 12. Divide 18 X 17 X 16 X 15 by 2x3x4x5x6. 13. A quantity of iron will make three hundred 30-lb. castings; how many 25-lb castings will it make? 14. Twenty reams of paper, of 20 quires each, and each quire 24 sheets, and each sheet making 24 pages, were made into books containing 160 pages each ; how many dozen books would there be? 15. How many hundred blocks 3 in. long, 2 in. wide, and 1 in. thick, can be made from a block 5 ft. long, 3 ft. wide, and 5 in. thick? FRACTIONS. ARTICLE 103. Reduction of Integers to Fractions of given Denominators. Reduce : 10. 200 to twelfths. 11. 37 to eighteenths. 12. 34 to fortieths. 13. 14 to twentieths. 14. 27 to thirteenths. 15. 31 to sixteenths. 16. 67 to twenty-seconds. 17. 19 to ninetieths. 18. 81 to twenty-ninths, 1. 2. 3. 4. 5. 6. 7, 8. 14 to sevenths. 23 to elevenths. 7 to twenty-thirds. 63 to eighteenths. 90 to ninths. 31 to thirty-seconds. 3 to fifty -sixths. 26 to eighths. 9, ol5 to ninths. 70 RAY'S NEW TEST EXAMPLES. ARTICLE 104. Case II. Reduce the following to Improper Fractions : 1. 15|. Q 1 Q 1 O. 1 ^ingf. 15. 562 T 3 f . 2. 19f 9. 28||. 16. 100^ 3. 991. 10. 45^. 17. 682}>, 4. 73 T V n"** ) fi . YOy 8 ^. 18. 129^f, 5. 36&. 12. 29^. 19. 29 T -f T . 6. 42 ji 13. 272ft. 20. 21 T V. 7. 176f 14, 396^ 4 T . 21. 73f|. ARTICLE 105. Case III. Reduce the following to Integers or Mixed Numbers 1. 4 7 . Q 2468 15. .a..o 2T? T2' 72 RAY'S NEW TEST EXAMPLES. 20. 21- 22. A. t, A, if- A, A, A, i- A, A> A>-A- 3 5 9 7 > TT> ?8> 3?- ji, A. I- f I, A, 7, T 3 r- f , $, A> A- 23. -A, A, &, &. 24. If, If, If, 1 T V 25- 2|, A, 3A, U- 26. H, H. H, 11- 27 4 A i 4 ' 7' 8' 9' IIP 28- if, 2, if, if, i 29- . 30. f, A. ARTICLE 110. Addition of Fractions. Case I. Add the following fractions: i- A. H, H, it- 2- T%> A> li> A- 3. 13. J.4 J.5 JL6. 5. ii, if, if, if. 6- 7 V, If, If, TV 7- ft, ft, It, It- ARTICLE 111. s. ft, n, it, ft- 9- if, if, li, If- 12- T 7 &, !* I 7 ? 7 ?, TTT> TT> TF 7 ;- //. Me following quantities : 2- 55 ~$i IT' H. tt. if- i, i, A- H if. tt |, 4, f . T V, A- H. T!' if 8- I, I, I, f 9- |, f, |, f 10. 4|, 3|, 8^, 6f. 11. 54, 6|, 5. 6- 7- 12. 12|, 16|, 13. 38|, 38A, 14. 1231,1351,147^,1501 15. 725^,871,931,691}. 16- |, f, I, |, |. 17- f f , |, f 18. H, H, H, H, lA- 19. 2 1, 2|, 2|, 2-1 2H. 20. If, If, 2|, 7|. 21. % 2^ 31, 4J. 22. A, A. A, A, A, 1- FRACTIONS. 73 23. If, If, If, li, ITV 24. 01 6f, 7f , 7f, 8f . 25. 1% 17f , 8H, 7 T \, 4J 26. If, If, 1 T \, 1 T %, If 27. f f, f, T \. 28. 234$, 236f , 2381, 2391 29. 12f, 124g, if, I7f, 181 30. If, If, If, 111 19ff- 914 192 _<, -34ft=? llf ARTICLE 113. Subtraction of Fractions. Case I. 1. From 18i take 2 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 168J 15. 2991 16. 17. 400 18. 736 19. 20. 365 - 37 21. 423if - - 237 22. 23. - 47H - 47f -367if 3-| 59 7 f =? 94. (^7^109 9QJ.47 V A*. Ji3j2^ **tYfr ARTICLE 114. Case II. 1. From | 2. From % 3. From j 4. From ^ 5. From | 6. From ^J- 7. From f| 8. From f 9. From j| 10. From ft 11. From 6 12. From 6| take |. take ^-. take -f$. take ^-. take T 5 ^. take T 7 5 . take ^. take |. take |f. take ft. take 2^ take 211 13. From 1^ take |f 14. From 15 T \ take 8. 15. From 8^ take 7f 16. From 13|| take 5 T V 17. From 6^ take J. 18. From 800 take 147|J. 19. From 728| take 149||. 20. From 24J| take 19Jf 21. From 48J| take 26f 22. From 432| take 329 T V 23. From 16980f take 7991-^-. 74 RAY'S NEW TEST EXAMPLES. ARTICLE 115. Multiplication of Fractions. Multiply together: 1- I, A 2- A. A- 3- M, it- 4- If, M- 5- it, tJ. ft 15 21 D< TT' TTF' 7 7 4 _6_ 8' ^' 2 1 * 8- !, ii If I, t, if- in 6 2ff S3 1U> TT> -JT' rr 11. V, , ff 12. 3-f, 2|. 13. 5i 61, 5. *^Ty~j ^T? "Q"" 15. 5i, 5^, 5-^. 16. 4f, 6, 3 17. 35|, 9. 18. i 150, 6 r V 19. 325, 10|. 20. 13f, 13|. 21. 15621, 1562^. 22. 3i, % % 23. 8, 7|, 5. 24. 4f , 5|, 5|, 3J. 25. 5i, 61, 74, 8f 26. A, 6, 4|, 5|. 27. 11 % H, 2|. 28. 8f, 3f, 7, 3|. 29. 2|, 2f, 2f, 2A- 30. 7, 7|, 8, 8J, 9. 31. 8, 8-|, 8|, 9. 32. T \, 3|, % % 6. ARTICLE 116. Fractional Parts of Integers. 1. What is -jJj- of 100? 2, What is f of 87? 3, What is f of 80? 4, What is if of 70? 5. What is 8 T of 9? 6. What is of 43? 7. What is If of 18? 8. What is ft of 72? 9. What is -jW of 17? 10. What is f| of 200? 11. What is i of 120? 12. What is J| of 67? ARTICLE 117. Compound Fractions. Reduce the following to Simple Fractions : 1. f of ||, 5. l-i of if. 2. -f of H. 6. |i of ||. 3. | of 2i 7. / r of - 2 ^. 4. f of 13|. 8. fj of llf FRACTIONS. 75 9. _y_ O f Y. 10. rto of A. 11. if of llf 12. | of | of 10t 13. | of | of 13i, o y o 16. A of 1 17. T \ of | 18. || of -i 19. of ; 20. if of \ - of 1 of 31. 04 o - of T \ of ^. -f of -%- of 6f - 7 T Of A Of f f J of | of 4|. 14. A of - t of 24f 21. it of M f ^ f 4 f 15. if of - [for f of 4f 22. foff of If of &* 23. ft of f of -| of H of 18i. B 24. -v- of Of 2T Of 130|. 25. if of it of |f of 4|. 26. ii of it of -y of 17|. 27. M of if of ft of 1% of 90. 28. of it of ti of 4 of 6 i- ARTICLE 118. Miscellaneous Examples. Find the cost : 1. Of 3f Ib. of sugar, at 8 ct. a Ib. 2. Of 5 yd. muslin, at 11^ ct. a yd. 3. Of 7| Ib. cheese, at 8 ct. a Ib. 4. Of 312^ Ib. of brass, at 27| ct. a Ib. 5. Of 4| yd. of fence, at $2| a yd. 6. Of \1\ Ib. of coffee, at $f a Ib. 7. Of 2| mi. of road, at $17200 a mi. 8. Of 18 bu. of potatoes, at $f a bu. 9. Of 38f Ib. of steel, at 12 ct. a Ib. 10. Of 6f Ib. of rice, at 6| ct. a Ib. 11. Of 13^ oz. of copper wire, at 7^ ct. an oz. 12. Of 4728 Ib. of pork, at 3f ct. a Ib. 13. From | of 17| take 1 of 17|. 14. To | of 52 add f O f 5f . 15. Multiply | of 7i by f of 7i. 16. How far can a boat move in 6| hours, at the rate of 13^ miles per hour? ^. 76 RAY'S NEW TEST EXAMPLES. 17. What cost 8-1- T. of hay, at $1G|- a T.? 18. A man owning 47^ A. of land, sold f of it ; how many acr.es has he remaining? 19. A man had 25| cords of wood, and burned | of it ; how much remains? 20. What cost 8000 torches at ct. each? 21. What would be the value of f of a farm of 58*- acres, at $7^ an acre? 22. A man earned $7^ a week, for 6|- weeks, and saved ^ of his wages; how much did he save? 23. An iron bar was 8^ feet long; ^ of it being broken off, the remainder was sold for 21 ct. a Ib. How much was received for it, the weight being 8^ Ib. per foot? 24. A had 57^ acres; B, 49^ acres; each gave the other of his own land; how much more had A then than B? ARTICLE 119. Division of Fractions. 1. Divide f by f. 16. Divide f by 25. 2. Divide f by |. 17. Divide 800 by T 8 T . 3. Divide 9 by 6f 18. Divide 15^ T by 4f 4. Divide 18 by 2f. 19. Divide 18| by 13^. 5. Divide 17$ by f 20. Divide 7j by If ' 6. Divide f by 20. 21. Divide 3^ by 4f 7. Divide 4 by 4f 22. Divide 675 by li. 8. Divide 19 T \ by 3f. 23. Divide 39 T V by 4}. 9. Divide 2$ by 5f 24. Divide 3964 by 4J. 6 J b 10. Divide 13^ by 4\, 25. Divide 13| by 47|. 11. Divide 27 by If 26. Divide 8| by 40o! 12. Divide 2| by 8. 27. Divide 67f by 3|. 13. Divide 19| by 4 T 4 T . 28. Divide 6| by llf 14. Divide 18f by 4^. 29. Divide 44589 by 39f 15. Divide 180 by 3f 30. Divide 347^ by 123|. FRACTIONS. 77 31. What cost 1 egg, at 17| ct. a dozen? 32. If 7 meir earn $243^, what will each man's share be? 33. A farm of 287f acres was divided among 5 chil- dren ; what would be the share of each ? 34. How much silk could be bought for $, at $3 a yard? 35. If 4| Ib. cheese cost 80 ct, find the cost of 1 Ib. 36. At 4-j^ ct. a Ib., how many pounds of rice can be bought for 75 ct.? 37. How much coffee, at 37^ ct. a pound, can be bought for 10 ct.? 38. How many apples, at ^ ct. each, can be bought for 15 cents? 39. How much saffron, at $16 an ounce, can be bought for If? 40. If 1^ oz. of quinine cost $4^, how much is that per ounce ? 41. At $2-| per day, how many days must a man work to earn $22i? 42. How much must a man charge per hour to receive $lf for 9 hours? 43. How many yards of muslin, at 6-| ct. a yd., can be bought for 80 ct.? 44. If 2% Ib. of butter cost $1^, how many pounds can be bought for $4? 45. A man chops 14^- C. in 4| da. ; how long will it lake him to chop 23| C.? ARTICLE 120. To find what part one number is of another. 1. 7-J- is what part of 20 ? 2. 16| is what part of 62 ? 3. | is what part of 28? 4. 4| is what part of 78 RAY'S NEW TEST EXAMPLES. 5. 7 T 3 ^ is what part of v^ : 6. 8f is what part of 105? 7. 19f is what part of 30|? 8. 84-f- is what part of 90f ? 9. What part of 102 is 4? 10. What part of 77$ is 3|? 11. What part of 91| is 13| ? 12. What part of 194 is 3f ? 13. | of 16| is what part of f of 34f ? 14. $ of 33| is what part of f of 50^ ? 15. |f of |f is what part of -^ of 90^? 16. -fa of 30 is what part of T ^ of 20|? ARTICLE 121. Reduction of Complex Fractions. Reduce the following to Simple Fractions : a 24| 4. 4 5. ^L e. 7 "" 8. J_. 9. 5lf 10. !t 84 954-' . t)9f 13. ^ 14. 109 15. 53f ARTICLE 122. 1. By what must 7^ be multiplied, to give the product ? 2. By what must 7 be divided to make the quotient FRACTIONS. 79 3. How many pounds of sugar can be bought for 42| ct., at 9-J- ct. a lb.? 4. Bought 5 1 A. of land for $77 ; what was the price per A.? 5. Divide f of ?i by f of ||. 6. I had 23| A. of land, and sold f. of it for $1045; how much was that per A.? 7. If 2^ yd. of cloth cost $3^, how much can be bought for $4? 8. If 2^ lb. of honey cost $f, how much can be bought for $10^? 9. How often will Li contain _ i? 10. A boy had $i, and spent -- of it for cherries; how many straps, at $^j each, can he buy with the balance of his money? 11. I am offered 141 A. for $1034 ; I have only $100 ; how many acres should I receive for my money? 12. Divide ?i by 1M. 04 J q 3 13. I had $43^, which I paid for gold at $ T 9 1J a pwt.; I had the gold made into rings weighing 1^ pwt. each; how many rings were made? 14. By what must L| be divided to make a quotient equal to _*? 15. By what must 10 be multiplied, so that the product may be y 1 ^? 16. I had 4^ bl. of glue, and gave J of my lot to my brother for $25-|; how much was that per bl.J^^ 17. If 7| yd. of cloth cost $16^, how manjr yards can be purchased for $28|? 80 KAY'S NEW TEST EXAMPLES. ARTICLE 123. Fractional Compound Numbers. 1. How many yards in 24 rcl.? 2. How many sq. yd. in 1 A.? 3. How many years in 14690 days? 4. What cost 141- \^ o f co ff ee at 2 7 ct. a lb.? 5. Eeduce 84 sq. rd. to sq. ft. 6. What cost 112| yd. of paving, at $8-J per rod.? 7. A field is 37 rd. long, and 25i rd. wide; how many sq. rd. in it? 8. What cost 1463 yd. of telegraph wire, at 20 ct. a rod? 9. How much will 43560 sq. yd. of land cost at $13.75 an acre? 10. What cost 51| bu. of wheat at 16 J ct. a peck? 11. Eeduce 12 yr. 300 da. to hr. Find the cost of: 12. 17| yd. of silk, at 87 ct. a yd. 13. 37^ bu. of potatoes, at 56| ct. a bu. 14. 26f yd. of tape, at 1 ct. a yd. 15. 6^ oz. of pepper, at 4J ct. an oz. 16. 18 lb. of ham, at 10J ct. a lb. 17. 14^ oz. of copper, at 2} ct. an oz. 18. Eeduce 53000 ft. to mi. 19. Eeduce 3 A. 120 sq. rd. to sq. yd. 20. Eeduce 127512 in. to mi. 21. How many sq. in. in 3 A.? 22. A field 93 rd. long contains 7 acres; how wide is it? 23. How many steps 2 ft. 9 in. long must be taken in going 5 mi.? 24. A glacier moves 2J in. in a day; how long will it take it to move one mile? FRACTIONS. 81 ARTICLES 124 AND 125. Reduction to Lower Denominations. 1. Reduce T |^ bu. to the fraction of a quart. 2. Eeducc -fa gal. to the fraction of a pint. 3. Reduce ^Vfr cw ^ *o ^ nc fraction of an oz. 4. Reduce -g^Vo" A. to the fraction of a sq. yd. 5. Reduce T |^ cu. yd. to the fraction of a cu. ft. 6. Reduce T ^ T yr. to the fraction of a day. 7. Reduce -fa Ib. to the fraction of an oz (Iron). 8. Reduce y^V^ Ib. to the fraction of a pwt. 9. Reduce T y 7 g to the fraction of a scruple. 10. Reduce y^Vfnr S( l- m ^- to the fraction of a sq. rd. 11. Reduce TTJ^TTTTTF cu - 7^. to the fraction of a cu. in. 12. Reduce -^-Q-^ da. to the fraction of a sec. 13. Reduce -g-^V^F ^ u - ^ ^ ne fraction of a pt. 14. Reduce y^y^or w ^- ^ ^ ne fraction of a min. 15. Reduce -fa gal. to the fraction of a gill. 16. Reduce i| gal. to integers. 17. Reduce T 7 T T. to integers. 18. Reduce ^ mi. to integers. 19. Reduce || A. to integers. 20. Reduce yr. to integers. 21. Reduce Ib. Troy to integers. 22. Reduce |f gal. to integers. 23. Reduce -J-jj- to integers. 24. Reduce ^ T. to integers. 25. Reduce ^^ mi. to integers. 26. Reduce y^ of a degree to integers. 27. Reduce y^-y sq. mi. to integers. 28. Reduce i chain to integers. 29. Reduce ff C. to integers. 30. Reduce ^ O. to integers. 31. Reduce |4 da. to integers. R. T. E.-6.* 82 RAY'S NEW TEST EXAMPLES. ARTICLE 126. Reduction to Higher Denominations. 1. Eeduce f min. to the fraction of a day. 2. Eeduce ^ cu. ft. to the fraction of a cord. 3. Eeduce -| sq. in. to the fraction of a sq. yd. 4. Eeduce f|- oz. to the fraction of a cwt. 5. Eeduce ^-| pt. to the fraction of a gal. 6. Eeduce &- pt. to the fraction of a bti. 7. Eeduce ^V S r - to the fraction of an oz. 8. Eeduce - 2 T 4 ^ 3 - cu. in. to the fraction of a cu. yd. 9. Eeduce | J) to the fraction of a pound. 10. Eeduce - 2 ^ yd. to the fraction of a mile. 11. Eeduce |^| sq. yd. to the fraction of a sq. mi. 12- Eeduce -|i hr. to the fraction of a year. 13. Eeduce f f Ib. to the fraction of a ton. 14. Eeduce - in. to the fraction of a chain. 15. Eeduce -^ gi. to the fraction of a gal. 16. Eeduce y 1 ^ qt. to the fraction of a bu. ARTICLE 127. 1. What part of 1 mi. 10 rd. is 88 rd.? 2. What part of 2 bu. 1 qt. is 1 bu. 2 qt. ? 3. What part of 9 C. is 16 cu. yd.? 4. What part of 39 Ib. is 7 Ib. 8 oz.? 5. What part of 1 wk. 5 da. is 1 da. 8 hr. 6. 3 A. 6 sq. yd. is what part of 9 A.? 7. 17 bu. 3 pk. 4 qt. is what part of 65 bu.? 8. 3 3 1 9 is what part of 5 g 2 9 ? 9. 8 yd. 1 ft. is what part of 5 rd. 1 yd. ? 10. 2 37' 30" is what part of 8 45'? 11. What part is 5 gal. 1 gi. of 10 gal.? 12. What part is 3 doz. and 6, of a gross? 13. What part is 12 Ib. 8 oz. of 2 T. 5 cwt.? FRACTIONS. 83 ARTICLE 128. 1. -ff sq. yd. f sq. ft.= ? 2. * c. -f 4 cu< y d. ~ ? 3. _f'=? ' ? 5. 3 T._ 4 cwt.? 6. f Cong. + f 0.=? 7. f mi. | rd. =? 4. ^ Ib. ^ oz. + | pwt.= ? 8. f chain J pace = ? 9. | wk. + 1 da. + | hr. =? 10. I bu. + | pk.+| qt. + | pt. = ? 1 1. -| gal. + f qt. + f pt. -j- f gi- = ? 12. T V T. + ^ cwt. 4 || Ib. =? 13. -jSj. mi. + ^ rd. + J yd. + J ft. =? 15. |f C. -f- -J-J cu. yd. -f- |f cu. ft. = ? ARTICLE 129. Promiscuous Examples. 1. From 8 take 2. Eeduce -% sq. mi. to integers. 3. Add 3J to the difference between 4^ and 6. 4. From 7| X 6f take 6f X 5f 5. Reduce | to a fraction whose denominator is 126. 6. Reduce yVrVg to its lowest terms. 7. Reduce f^$ to twentieths. 8. Find a number which multiplied by 8J gives 60. 9. What number divided by 4^ gives 4^? 10. From |-f--| take f -f-f 11. Reduce T 7 T to a fraction whose numerator is 77. 12. What part of $5 is 4 of 5 cents? 13. Reduce yy^TT ^ ^ ^ ne fraction of a pound. 14. $4J will buy 1| yd. of cloth ; how much will If yd. cost? 15. Bought 3750 Ib. of iron, at $3.50 per cwt.; what is the amount of the bill ? 84 RAY'S NEW TEST EXAMPLES. 16. A boy works 3 days at the rate of $5f a week; how much does he earn? 17. I have 55 A. of land, worth $17^ an acre; B wishes to trade me 7 hogs, worth $7-|- each ; what part of my land should be given for them ? 18. Bought 32 T. of iron for $1218.75; at that rate, what quantity can I buy for $1000? 19. A man lost $13J, and borrowed $57f; he then had $106^; what sum had he at first? 20. What number is as much greater than 15 J as 15J is greater than 7 T ^-? 21. A farmer raised 208 bu. 1 pk. of wheat, and sold 119 bu. ; what part of his crop has he remaining? 22. A lady bought 35^ yd. carpet for $47; had she bought 6 yd. more, what would the bill have been? 23. A farm is worth $5500, and A owns -f^ of it ; what part of his share should A sell for $825? 24. How much would a family consume in August, at the rate of 8 Ib. 5 oz. daily? 25. f of a certain number is 389^; what is the number? 26. Multiply 4f X 8| by 2^ X 3f . 27. A farmer sold T 4 T of his flock of geese, and has 14 dozen remaining; how many geese had he at first? 23. Reduce 12. ill, -11 and _Zl to a common denom- 8|' 12f' 12fi llf inator. 29. Hats cost $31 apiece, but late in the season are sold at |- of the cost; how many can I then buy for $48? 30. Sold a house for $2373, which was -J of the cost ; how much did I lose? 31. A lawyer collected $18.80, and kept f of it ; how much did he pay over? 32. What number is that, to which, if you add | of itself, the sum will be FRACTIONS. 85 33. Find the value of a lot 88 ft. long and 49J ft. wide, at $700 per acre. 34. f of a farm are worth $3157^r; what are f of it worth ? 35. 53^ yards of cloth cost me $88; what will I lose by selling 8| yd. for $10? 36. Three men found a sum of money, of which the first took , and the second -|, leaving the third man $69.44; what was the sum found? 37. A expended $347 for land, at $-f an acre ; and B, $4243 for land, at $5J an acre ; how many acres have both together? 38. What was the cost of 47 head of cattle, if $47 was lost by selling 13 head for $26^ apiece? 39. From a lot 100 rd. long and 72 J rd. wide, was sold a lot 45 rd. long and 29 rd. wide; what part of the whole lot was sold? 40. A owns 405 A. 39 sq. rd., and B owns 391 A. 109 sq. rd. ; how much land must A sell B, so that their farms may be of equal size? ARTICLE 130. Practice. Find the cost of : 1. 450 Ib. butter, at 25 ct. a pound. 2. 784 yd. muslin, at 6J ct. a yard. 3. 462 gal. vinegar, at 16 f ct. a gallon. 4. 673 yd. delaine, at 62 ct, a yard. 5. 96 gal. wine, at $1.87-| ct. a gallon. 6. 5726 Ib. whiting, at 1^ ct. a pound. 7. 538 bu. wheat, at $1.12^ a bushel. 8. 788 yd. cloth, at $1.62 a yard. 9. 375 Ib. cheese, at 8^ ct. a pound. 10. 424 A. land, at $3.18f an acre. 86 BAY'S NEW TEST EXAMPLES. 11. 398 bu. barley, at 75 ct. a bushel. 12. 666 Ib. feathers, at 33 ct. a pound. 13. 78 C. wood, at $4.75 a cord. 14. 3786 Ib. twine, at 16| ct. a pound. 15. 5 gal. 3 qt, of brandy, at $2.50 a gallon. 16. 17 yd. 2 ft. of paving, at $2.40 a yard. 17. 69 bu. 3 pk. of potatoes, at 68 ct. a bushel. 18. 4 Ib. 11 oz. of honey, at 36 ct. a pound. 19. 3 hr. 45 min. work, at 40 ct. an hour. 20. 7 oz. 7 pwt. of silver, at 88 ct. an ounce. 21. 3 bu. 3 pk. of clover seed, at $3.60 a bushel. 22. 49 sq. yd. 6 sq. ft. of plastering, at 27 ct. a square yard. 23. 3 g 2 % 1 9 of quinine, at $3.60 an ounce. 24. 4 bu. 2 pk. 5 qt. of berries, at $3.20 a bushel. 25. 15 gal. 3 qt. 1 pt. 1 gi. of wine, at $1.92 a gallon. 26. 5 C. 96 cu. ft. of wood, at $4.40 a cord. 27. How many bushels of oats, at 37 J ct. a bu., can be bought for $7.87? 28. How much cloth, at $2.12^ a yard, can be bought for $90.31J? 29. What cost 18 Ib. 12 oz. of coffee, at 331 c t. a Ib.? 30. Find the cost of 500 screws, at 36 ct. a gross. 31. Find the cost of 18 bu. 2 pk. of apples, at $.66| a bushel. 32. What cost 40 rubbers, at 40 cents a dozen? 33. At $3.37^ an acre, how many acres of ground can be bought for $281.25? 34. What cost 5 bu. 2 pk. of strawberries, at 33^ ct. a quart? 35. A week's work is 6 da., of 10 hr. each; how much can a man earn in 4 da. 6 hr., if his weekly wages are $10.50? 36. Find the cost of 11 T. 940 Ib. of hay, at $12 a ton. DECIMAL FRACTIONS. 87 DECIMAL FRACTIONS. ARTICLE 135. Writing Decimals. Write the following Decimal Numbers : 1. 803 thousandths. 2. Fifty-one thousandths. 3. Nine thousandths. 4. Forty-six ten-thousandths. 5. Two hundred and one ten-thousandths. 6. 7735 hundred thousandths. 7. 86 hundred-thousandths. 8. 3 hundred-thousandths. 9. Nine hundred and nineteen thousandths. 10. Nine thousand and twenty ten-thousandths. 11. Ten thousand and one hundred-thousandths. 12. Five thousand and sixty-seven ten-thousandths. 13. 381257 millionths. 14. 40703 millionths. 15. 2008 millionths. 16. 88 millionths. 17. 7 millionths. 18. Forty seven thousand and eighteen millionths. 19. Five hundred and fifty-five millionths. 20. Three hundred thousand and eight millionths. 21. Sixty-seven millionths. 22. Fifty-seven tenths. 23. 2406391 ten -millionths. 24. 65400 ten-millionths. 25. 49 ten-millionths. 26. 880004 ten-millionths. 27. 6 ten-millionths. 28. 31000722 ten-millionths. 29. Four hundred and eighty hundredths. 88 RAY'S NEW TEST EXAMPLES. i 30. 14 units and 5 hundredths. 31. 3 units and 17 thousandths. 32. 3000 units and 4 thousandths. 33. 3004 thousandths. 34. 8354 hundredths. 35. One wmY and one millionth. 36. One million wmYs and one millionth. 37. Three hundred millionths. 38. Seven hundred units and seven hundredths. 39. 19 bilUonths. 40. 39704 ten-billionths. 41. 800004 hundred-millionths. 42. Eight thousand and five tenths. 43. Eight thousand wwYs and five ten-thousandths. 44. 379000 M/uYs and 379 thousandths. 45. Fifty thousand and one hundred bilUonths. ^"' TTT> T0TF> TlFlnF' TTFTT' TTOTRr 47- T 8 A> Tr(Hro> TTTOTI> T"ofiTrTr? fir- 48. 5^, 16 r ^, 200^, 30^-30^. ARTICLE 136. Reading Decimals. Head the following Decimal Numbers : 1. 4.18; 6.008; .0006; 36.036; 3.4075. 2. .702; .078; .02005; 50.09; .0006. 3. .00066; .30066; .00456; .000036. 4. .01 ; .016 ; .0162 ; .01624. 5. 4736.2 ; 3.8914 ; .356 ; 283.67. 6. 2000.20002 ; 304.0506 ; 7.24006. 7. .3703 ; 3.703 ; 37.03 ; 370.3. 8. 4.4; 4.04; 4.004; 4.0004. 9. .056 ; 30.07 ; .00009 ; .010203. 10. 45.0009 ; .005009 ; 60.016. 11. 37.03; 4638.9; 364.005. DECIMAL FRACTIONS. 89 12. .0102; .001002; .00010002. 13. 5.806 ; 50.4903 ; 6.8938. 14. 3700.0004; .3704; 3000.0704. Change the following to Common Fractions : 15. .64; .165; .0375; .9375. 16. .024; .00008; .0000088. 17. .875; .4375; .15625. 18. .1024; .83875; .873642. ARTICLE 141. Reduction of Decimals. Case III. Reduce the following to Common Fractions or Mixed Numbers : 1. .875. 9. .975. 17. 300.25. 2. .64. 10. .0084. 18. 46.875. 3 .512. 11. .1875. 19. 13.92. 4. .625. 12. .46875. 20. 20.02. 5. .025. 13. 4.045. 21. .6875. 6. .256. 14. 26.18. 22. 14.01875. 7. .0025. 15. .0125. 23. 9.008. 8. .2224. 16. 19.625. 24. .34375. ARTICLE 142. Reduction of Decimals. Case IV. Reduce the following to Decimals : i. f. 2. A- 3- A- * tt- Mi e. if 7- if 8- if T61F- ** 10. 11- 12- dfr 13- Tfrr. i*. m> 16. 17- IS- 18. ft- 19. |f. 20. n- 21. If. 22. |f. 23. ^ a*- 90 RAY'S NEW TEST EXAMPLES. ARTICLE 143. Addition of Decimals. 1. Add 3.12; 41.3; 68.94; 39.77. 2. 18 and 54 hundredths -j- 19 and 5 tenths + 53 and 73 hundredths -f- 37 and 56 hundredths + 16 and 9 tenths =? 3. 5 and 17 thousandths + 73 and 29 hundredths + 128 and 3 tenths + 94 and 983 thousandths -f- 26 and 71 hundredths + 271 and 7 tenths = ? 4. Add 413 thousandths ; 413 ten-thousandths ; 413 hundred-thousandths, and 413 millionths. 5. 25.7 + 6.009 + .4309 -f 509.7 + 38.08 + 8.983 + 73.38 = ? 6. Add 46 and 89 thousandths; 60 and 894 thou- sandths; 8 and 946 thousandths; 9 and 468 thousandths; 89 and 46 thousandths ; 460 and 89 thousandths, and 20. 7. Add 400.009; 40.09; 4.0009; 40.9; 400.09; 4.009; 100; and .002. 8. 738.84 + 388.47 + 884.73 + 847.38 + 473.88+59.99+ 59.099 + 99.59 = ? 9. Add 17.38; 18.37; 19.36; 20.35; 21.34; 22.33; 23.32 ; 24.31 and 25.3. 10. Write 395.4276 seven times and add. 11. Write 234.056 eight times and add. 12. Add 893 thousandths; 753 hundredths; 49 tenths; 3739 thousandths; 5 hundredths; 55 hundredths; 5500, and 127 thousandths. 13. 46.8 + 48.6 + 68.4 + 64.8 + 84.6 + 86.4 + 44.4 + 66.6 + 88.8 = ? 14. Add 74 and 8 ten-thousandths; 36 and 5-thou- sandths; 637 and 4 ten-millionths; 29 and 8 tenths; 3 and 8914 hundred-thousandths; 55 and 93 hundredths; 84 millionths, and 637 and 27306 ten-millionths. DECIMAL FKACTIONS. 91 ARTICLE 144. Subtraction of Decimals. . 1. From 47.378 take 19.89. 2. From 60.06 take 50.89. 3. From 48.937 take 13.0609. 4. From 300 take 46.875. 5. From 345.6789 take 88.88. 6. Take 8.76 from 234.372. 7. Take 23.9564 from 32.404. 8. Take 22.222 from 111.11. 9. Take 6.0008 from 22.93004. Find the difference between the following: 10. 39.81 and 20.985. 11. 100.001 and 50.09. 12. 324.137 and 199.9994. 13. 64 thousandths and 64 hundredths. 14. From 147 and 39602 hundred-thousandths take 58 and 545986 millionths. 15. Take 73421 and 397 ten-thousandths from 124316 and 397 thousandths. ARTICLE 147. Multiplication of Decimals. Multiply : 1. .643 by .89. 2. 3 56 by 62.5. 3. 7.875 by 94. 4. .125 by .126. 5. 48.76 by 48.75. 6. .03 by .02. 7. .744 by .125. 8. .0375 by .036. 9. 9.9 X -098. 10. 666. X 5-55. 1 1. .048 X .04375. 12. .9375 x 2400. 13. 7.39 X .0043. 14. .2502 X ^848. 15. 42.075 X % 16. 3.956 X 4 ^ljL 92 RAY'S NEW TEST EXAMPLES. 17. Multiply 48 units and 75 hundredths by 6 units and 32^ thousandths. 18. Multiply 893 thousandths by 893 ten-thousandths. 19. Multiply 38400 by 19 units and 28 thousandths. 20. Multiply 27 thousand by 27 thousandths. 21. Multiply 78 and 125 thousandths by 1024. 22. Multiply 67 thousand 2 hundred by 67 and 2 hun- dredths. 23. Multiply 7936 ten-thousandths by 390 and 625 thousandths. 24. Multiply 6.625 by 14.32. ARTICLE 150. Division of Decimals. Divide : 1. 5.845 by 3.5. 2. 9.4125 by 1.25. 3. .7614 by .36. 4. 2.875 by 1.15. 5. 4.752 by 198. 6. .897 by .06. 7. .897 by 260. 8. .7375 by .059. 9. 1287.7651 by 3.217. 10. 160 by .04. 11. 6.5667 by 31.27. 12. 17429.1 by .4251. 13. 3.1 by 3.2. 14. .004 by 160. 15. 8.91 by 1.98. 16. 1 bv 16. 17. Divide 37 units and 37 thousandths by 4 units and 4 thousandths. 18. Divide 12 units and 12 hundredths by 16 units and 16 hundredths. 19. Divide 1 hundred by 1 hundredth. 20. Divide 208 millionths by 65 hundred-thousandths. 21. Divide 8.76 by 132. 22. Divide .9 by 2.99. 23. Divide .001 by 150. 24. Divide 27.5 by .28. DECIMAL FKACTIONS. 93 DECIMAL COMPOUND NUMBERS. ARTICLE 151. Reduction to Lower Denomination. 1. Reduce .0125 bu. to the decimal of a pint. 2. Reduce .0273 gal. to the decimal of a pint. 3. Reduce .00043 T. to the decimal of a pound. 4. Reduce .0275 yd. to the decimal of an inch. 5. Reduce .0000075 sq. mi. to the decimal of a sq. rd. 6. Reduce .0000025 cu. yd. to the decimal of a cu. in. 7. Reduce .00001125 da. to the decimal of a second. 8. Reduce .00375 C. to the decimal of a cu. ft. 9. Reduce .000575 sq. yd. to the decimal of a sq. in. ARTICLE 152. Reduction of Decimals to Integers. Find the value of the following, in Integers : 1. .4375 bu. 2. .4375 gal. 3. .15625 T. 4. .15625 mi. 5. .390625 sq. mi. 6. .7 C. 7. .38 yr. 8. .047 of a circle. ARTICLE 153. Reduction to Higher Denominations. 1. Reduce .352 pt. to the decimal of a bushel. 2. Reduce .48 gi. to the decimal of a gallon. 3. Reduce .648 sq. in. to the decimal of a sq. yd. 4. Reduce .5832 cu. in. to the decimal of a cu. yd. 5. Reduce .472 qt. to the decimal of a bushel. 6. Reduce .486 min. to the decimal of a day. 7. Reduce .4096 oz. to the decimal of a cwt. 8. Reduce .39 pt. to the decimal of a gallon. 9. Reduce .1296 sec. to the decimal of a day. 10. Reduce .015 pt. to the decimal of a bushel. 94 KAY'S NEW TEST EXAMPLES. 11. Reduce .13824 cu. in. to the decimal of a cord. 12. Eeduce .17532 hr. to the decimal of a year. 13. Eeduce .792 in. to the decimal of a mile. 14. Eeduce 7.68 oz. to the decimal of a ton. 15. Eeduce .17424 sq. in. to the decimal of an acre. ARTICLE 154. Promiscuous Examples. 1. Find the value of .05 da. in integers. 2. If 3.7 yards cost $10.36, what will 5.8 yards cost? 3. If 3.5 acres of land cost $430.43, how many acres could be bought for $614.90? 4. Find the cost of 4 bu. 3 pk. of oats, at 46 cents a bushel. 5. A man sold 55 gal. 1 pt. of wine, at $1.80 a gallon, and was paid in tea at 84 ct. a pound; how many pounds did he receive? 6. A field 40 rods wide contains 10 A. 80 sq. rd.; how long is it? 7. How much wood, at $2.90 a cord, can be bought for $105.125? 8. .4 mi. + .3 rd. -f .7 yd. ==? 9. Find the value of .7475 T. in integers. 10. How much vinegar, at 24 ct. a gallon, can be bought for $7.77? 11. What cost 1000 cu. yd. of embankment, at the rate of $0.37 per cu. ft.? 12. Find the value of .234375 bu. in integers. 13. What cost 7227 feet of wire fence, at 14 ct. a rod? 14. A locomotive runs 17 mi. 32 rd. in an hour ; how far will it run in 13 hr. 39 min.? 15. .1 yr. + .2 wk. + .3 da, + .4 hr. == ? 16. Eeduce 4 of _U to a decimal. 16 17. 1.4 bu. 3.7 pk.=? THE METRIC SYSTEM. 95 18. How much land, at $500 an acre, can be bought for $131.25? 19. .03 T. + .73 cwt. + .75 lb.=? 20. Find the cost of 7 Ib. 7 oz. of silverware, at $1.20 an ounce. 21. How much cloth, at $1.44 a yd., must be given for 6 bu. 6 qt. of strawberries, worth $4.80 a bushel? 22. At 12^ ct. a pound, how much cheese can be bought for $19.81? 23. What cost 4350 Ib. iron, at $2.80 a hundred pounds? 24. What cost 8764 pickles, at 75 ct. a hundred ? 25. What cost 108 screws, at $1.08 per gross? 26. Find the value of .77 yr. in integers. 27. A locomotive runs 16 mi. 256 rd. per hour; how long will it be in running 154 mi. 280 rd. ? 28. A man can earn 18| ct. per hour, and a boy 12^ ct. ; how much will the man earn while the boy earns 29. Grading a road cost $10312.50, at 62 ct. 5 m. per foot; how long is the road? 30. Find the value of a lot 70 rods square, at $20 an acre. Reduce : THE METRIC SYSTEM. ARTICLE 156. Measures of Length. 1. 394.5 Hm. to dm. 2. 93.64 m. to kilometers. 3. 1234.56 Dm. to Mm. 4. 987.65 Km. to Dm. 5. .34 m. to myriameters. 6. 74.6 Dm. to cm. 7. 83.7 Hm. to Mm. 8. .37 Mm. to meters. 9. 4600 Km. to dm. 10. 58000 cm. to Hm. 11. 374.5 Mm. to cm. 12. 67.25 Dm. to Km. 13. 8936.4 cm. to Dm. 14. .456 Km. to Hm. RAY'S NEW TEST EXAMPLES. ARTICLE 157. Metric Square Measure. Reduce : 1. 374680 ni 2 to hektars. 2. 493.2 A. to centars. 3. 387.43 ca. to ars. 4. 387.43 m 2 to ars. 5. 43.875 A. to m 2 . 6. .457 ca. to hektars. 7. 8973.4 m 2 to hektars. 8. 5839 A. to m 2 . 9. 3843 ca. to hektars. 10. 3970 A. to centars. ARTICLE 158. Measures Reduce : 1. 4800 cl. to liters. 10. 2. 39.5 Dl. to centiliters. 11. 3. 493.7 dl. to HI. 12. 4. 58.39 HI. to centiliters. 13. 5. .457 Dl. to liters. 14. 6. 6.789 1. to centiliters. 15. 7. 34.692 HI. to Dl. 16. 8. 42.789 dl. to liters. 17. 9. 325.84 1. to hektoliters. 18. of Capacity. 4.7 dl. to dekaliters. 3800 HI. to deciliters. 29.7 1. to dekaliters. 468.3 cl. to hektoliters. 38700 Dl. to deciliters. 49 m 3 to liters. 37282 cL to m 3 . ' 678 1. to cubic meters. .0303 m 3 to deciliters. ARTICLE 159. Reduce: 1. 6.5 Mg. to M. T. 2. 489.31 Dg. to mg. 3. .04653 Q. to Dg. 4. 654.3 Hg. to quintals. 5. 87 M. T. to kilograms. 6. .937 mg. to grams. 7. 123.456 Hg. to dg. 8. 873.4 dg. to Dg. 9. 88.736 Mg. to eg. 10. .0086 g. to quintals 11. .0765 Kg. to M. T. Metric Weights. 12. 3945 eg. to Hg. 13. 3.894 M. T. to grams. 14. 87300 Kg. to mg. 15. 89900 Dg. to Mg. 16. .00489 Q. to dg. 17. 4000 G. to Mg. 18. 12000000 mg. to K#. 19. 9876541 dg. to quintals. 20. 34.56 Kg. to grams. 21. 48004800 eg. to Hg. 22. .09083 M. T. to mg. THE METRIC SYSTEM. 97 ARTICLE 160. Find the value of: 1. 40 meters. 2. 50 hektars. 3. 375 kilograms. 4. .6375 kilometers. 5. 13 tonneaux. Reduce : 11. 45 hektoliters to bu. 12. 100 inches to meters. 13. 100 mi. to kilometers. 14. 100 sq. yd. to m 2 . 15. 100 acres to hektars. 16. 100 cu. yd. to m 3 . 17. 48 sq. rd. to ars. 18. 18 T. to metric tons. 6. 93.75 sters. 7. 875 grams. 8. 500 cubic meters. 9. 625 square meters. 10. 37.5 ars. 19. 454 bu. to hektoliters. 20. 66 gal. to liters. 21. 1 Ib. 4oz. 1 pwt. 12 gr. to grams. 22. 3000 sq. ft. to m 2 . 23. 56 bu. 3 pk. to HI. 21 2 Ib 8 3 1 3 12 gr. to the metric system. ARTICLE 161. Miscellaneous Examples. 1. What cost 475 kilos of iron, at 4 ct. a pound? 2. What cost 6 hektometers of fence, at 15 ct. a foot? 3. What cost 40 sters of wood, at $6.25 per cord ? 4. What cost 327 cubic meters of stone-work, at $5.30 per cubic yard ? 5. Find the weight of a stone 4 m. long, 4 dm. wide, and 8 cm. thick, if a cubic meter weighs 3 cwt. 6. What cost a field 300 meters square, at $30 per ar? 7. What cost a pile of wood 8 m. long, 3 m. wide, and 1.5 m. high, at $1.30 per ster ? 8. What must be paid for 17 quintals of wheat, at 5 ct. per kilo? 9. A field is 52 yd. wide and 92 yd. long; what is it worth, at $.35 per square meter? R. T. E. 7. 98 RAY'S NEW TEST EXAMPLES. 10. A pile of stone is 109 ft. long, 36 ft. wide, and 9 ft. high; what is it worth at $3.80 per cubic meter? 11. Find the cost of 64.3 Ib. of gold ore, at 45 ct. per gram. 12. Find the cost of a gold chain weighing 1929 grains, at 60 ct. a gram. 13. What would be the cost of 2 T. 15 cwt. 11 Ib. 8 oz. of coal, at $5.60 per metric ton? 14. How long will it take a man to walk 31.0685 mi. if he can walk 6 kilometers in an hour? PERCENT AG E. ARTICLE 164. Case I. Find the following : 1. 28 % of 925. 2. 25 % of 624. 3. 23 % of 900. 4. 13 % of 744. 5. 16| % of 390. 6. 37| % of 8.8. 7. 2 % of 290. JFAa* w : 15. 22% of 1800 bu. corn? 16. 85% of 7 da,? 17. T V% of $480? 18. 500% of 71 A.? 19. 53% of 3 T.? 20. 20% of 19 gal 1 qt. 1 pt.? 8. A % of 70. 9. 14f % of 1393. 10. 56 % of 750. 11. 5.6 % of 750. 12. \ % of 467. 13. 800 % of 800. 14. 900 % of 21. 3 bu. 2 100% of pk.? 22. 66 % of 87 gal.? 23. \% of |? 24. 2|% of 2^? 25. 16f% of 16 2? 26. 77% of 187.05? PERCENTAGE. 99 ARTICLE 165. Case II. 1. What per- cent of 275 is 33? 2. What per cent of 48 is 36? 3. What per cent of 60 is 10.2? 4. What per cent of 800 is 600? 5. What per cent of 666 is 499.5? 6. What per cent of 350 is 56 ? 7. What per cent of 75 bu. is 33 bu. ? 8. What per cent of 48 is 96? 9. What per cent of 56 is 560 ? 10. 172i is what per cent of 230? 11. 187.5 is what per cent of 150? 12. .5 is what per cent of 250? 13. 4 is what per cent of 17|? 14. 2.3 is what per cent of 18f ? 15. .014 is what per cent of 70? 16. 29 is wnat per cent of 80? 17. 1 bu. 2 pk. is what per cent of 3 bu. 3 pk. ? 18. 6 gal. 3 qt. is what per cent of 4 gal. 2 qt. ? 19. What per cent of ^ is ? 20. What per cent of 1 wk. is 4 da. 4 hr. 48 min.? ARTICLE 166. Case III. 1. 4.2 is 6% of what number? 2. 153 is 68% of what number? 3. 315 is \^. 16. A note of $500, dated July 26, 1870, payable in 90 days, and discounted Aug. 5, 1870, at 12^. 17. A note of $450, dated Jan. 19, 1880, payable in 3 months, and discounted Feb. 16, at 4%. 18. A note of $720, dated Oct. 14, 1875, payable in 90 days, and discounted Nov. 21, 1875, at 5%. 19. A note of $360, dated May 19, 1877, payable in 3 months, and discounted June 26, 1877, at 4%. 20. A note of $360, dated May 19, 1877, payable in 90 days, and discounted June 26, 1877, at 4%. 21. A note of $783.29, dated April 22, 1875, payable in 80 days, and discounted June 3, 1875, at 9%. 22. A note of $400, dated Dec. 16, 1883, payable in 4 months, with interest at 6^, and discounted Feb. 13, 1884, at 9%. 23. A note of $720, dated Jan. 13, 1846, payable in 90 days, with interest at 10%, and discounted March 3, 1846, at 9^. 24. A note of $600, dated March 2, 1884, payable in 8 mo. 7 da., with interest at 9%, and discounted July 14, 1884, at 12fi. 25. A note of $450, dated Sept. 19, 1882, payable in 9 mo. 27 da., with interest at 5%, and discounted Jan. 20, 1883, at 8%. 26. A note of $5000, dated June 16, 1888, payable in 90 days, with interest at 6%, and discounted July 16, 1888, at 8%. 27. A note of $475, dated Jan. 1, 1880, payable in 4 months, with interest at 4%, and discounted Jan. 15, 1880, at 10%. 124 RAY'S NEW TEST EXAMPLES. ARTICLE 197. Case II. 1. The proceeds of a note, payable in 60 days, dis- counted at a bank at 6%, were $494.75. Find the face of the note. 2. A note payable in 30 days was discounted in bank at 8% ; the proceeds were $595.60. What was the face of the note? 3. For what sum must I make a note at 60 days, to obtain $739.50 from a bank discounting at 8%? 4. I wish to obtain $800 on a note payable in 42 days ; for what sum must I give my note to a bank dis- counting at 4% ? 5. For what sum must I give a 60-day note, to obtain $1000 from a bank discounting at 9^ ? 6. Sold 40 acres of land, receiving a note at 6 months, which I at once discounted in bank at 6%, receiving $2326.80; what was the price per acre? 7. I sold 20 horses, receiving a note payable in 3 months, for which I received $2338 from a bank dis- counting at 10% ; what was the price of each horse? 8. A note dated May 3, 1885, payable in 6 months, and drawing 6% interest, was discounted in bank Sept. 27, 1885, at 9%, the proceeds being $2040.39; what was the face of the note? ARTICLE 199. True Discount. What is the present icorth and discount, at 6%, of: 1. $450.00, due in 3 yr. 4 mo.? 2. $900.00, due in 7 yr. 4 mo.? 3. $685.00, due in 6 yr. 2 mo.? 4. $810.00, due in 2 yr. 1 mo.? 5. $359.00, due in 3 yr. 3 mo. 10 da.? DISCOUNT. 125 6. $448.70, due in 1 yr. 1 mo. 20 da.? 7. $622.30, due in 8 yr. 10 da.? 8. $373.10, due in 5 yr. 6 mo. 15 da,? 9. $616.21, due in 7 yr. 9 mo. 13 da.? 10. $888.00, due in 8 yr. 8 mo. 8 da.? Find the true discount, at 6%, of: 11. $961.00, due in 4 yr. 12. $427.00, due in 3 yr. 8 mo. 13. $262.80, due in 1 yr. 7 mo. 14. $490.10, due in 4 yr. 3 mo. 10 da. 15. $161.21, due in 2 yr. 6 mo. 9 da. 16. $3836.90, due in 2 yr. 1 mo. 21 da. 17. $936.43, due in 6 yr. 11 mo. 23 da. 18. $700.00, due in 9 mo. 13 da. 19. $1000.10, due in 27 da. 20. A bill of merchandise amounted to $364, at 4 months time, or 4% off for cash ; if money is worth 12% per annum, how much will the buyer gain by paying cash ? 21. What should be paid May 10, 1884, for a debt of $264.20, due Jan. 15, 1886, money being worth 6%? 22. A debt of $1368 is due in 2 years : how much more should be given for it, if money is worth 7%, than if money is worth 10%? 23. A balance of $514.80 is due: one third in 1 yr., one third in 2 yr., and the balance in 3 yr. What sum should pay it now, money being worth 10%? 24. What debt could be settled by paying $561.60 cash, and giving two notes, of $561.60 each, one payable in 6 mo., and the other in 1 yr., money being worth 8%? 25. A lot was bought for $1800, one third cash, one third in 1 yr., and one third in 2 yr., with interest at 6%. If money is worth 10%, what sum in cash should have been paid for the lot? 126 KAY'S NEW TEST EXAMPLES. ARTICLE 201. Domestic Exchange. 1. New York exchange being \% premium, what must be paid for a sight draft on that place for $4700? 2. What must be paid for a sight draft on San Fran- cisco for $730, at \% discount? 3. Find the cost of a sight draft on Philadelphia for $4950, at 2^% premium. 4. Find the cost of a sight draft on Toronto for $1360, at \^ discount. 5. What must be paid for a -sight draft on Milwaukee for $373.84, at \% premium? 6. What will be the cost of a sight draft on Santa Fe for $2377.50, at \% discount? 7. What must be paid for a draft on New York for $1000, payable in 30 days, exchange at par, and interest 6#? 8. What must be paid for a draft on Boston for $1000, payable in 30 days, exchange being at \% dis- count, and interest 6%? 9. Find the cost of a 30-day draft on Savannah for $2400, exchange at \% discount, interest at 8%. 10. What cost a 60-day draft on Cleveland for $1500, exchange at \% premium, interest at 8%? 1 1. What was the face of a sight draft for which $796 was paid, exchange at \^ discount? 12. What w r as the face of a 60-day draft on New York, for which $792 was paid, exchange being -^^ premium, and interest 6% ? 13. What was the face of a 90-day draft on Mobile costing $1857.83, exchange being at \% premium, in- terest at 8% ? 14. $1000 was paid for a sight draft on Detroit, ex- change at \% discount; what was the face of the draft? INSURANCE. 127 ARTICLE 202. Foreign Exchange. 1. What must be paid for a bill of exchange on Lon- don for 796 5s., exchange being at $4.84? 2. What will be the cost of a bill of exchange on Edinburgh for 283 15 s., exchange being at $4.88? 3. How large a bill on Manchester can be bought for $5314.41, exchange being at $4.86? 4. How large a bill on Marseilles can be bought for $818.75, exchange being at 5 fr. 16 centimes? 5. What cost a bill on Havre for 5047 francs, ex- change being at 5 fr. 15 centimes? 6. What cost a bill on Munich for 4800 reichsmarks, exchange being 96 cents for 4 reichsmarks? 7. What cost a bill on Dresden for 3742 reichsmarks, exchange being at $.98? 8. How large a bill on Stuttgart can be bought for $1000, exchange being at $.965? INSURANCE. ARTICLE 204. Fire and Marine Insurance. 1. What must be paid for $4800 insurance on a dwell- ing at ^7 2. A factory is valued at $18000; what must be paid for insuring l of its value, at f% ? 3. What will be the premium for insuring % of a steamer valued at $36800, at \% ? 4. A store is valued at $15000, and the contents at $11000; what will be the premium for insuring | of the value of the store, at |%, and | of the value of the con- tents, at \%'l 128 RAY'S NEW TEST EXAMPLES. 5. Insured a mill for f of its value, at f%, the premium being $41.25; what was the value of the* mill? 6. A merchant has goods valued at $46000, and pays $184 for insurance at \% ; what part of the value is in- sured? 7. I insured f of a factory, valued at $35400, and | of the stock, valued at $41200, paying $436; what was the rate of insurance? ARTICLE 205. Life Insurance. 1. What must be paid yearly for $6000 life insurance, the premium being $32.18 per $1000? 2. A man paid $382.50 for 5 years insurance on a life policy for $3000; what was the company's annual rate per $1000? 3. A father, at the age of 50, insures his life for $5000, at $47.18 per $1000 annually ; his son, aged 21, insures his life for the same sum, at an annual rate of $19.89. If each lives to the age of 71, which will pay the greater sum for insurance, and how much more than the other will he pay? 4. An endowment policy for $2000 costs $107.32 per $1000 annually, for 10 years; what would be the amount of the ten payments, allowing simple interest at 6% ? TAXES. ARTICLE 208. To fix the Rate of Taxation. 1, A tax of $625000 is to be levied upon a valuation of $250000000 ; what will be the rate of taxation ? 2, The valuation in a certain city being $165000000, and the amount of tax to be levied $3795000, what will be the rate of taxation ? TAXES. 129 3. The expense of building a school-house was esti- mated at $6600, to be raised by a tax of 2^ mills on $1 ; what is the valuation? 4. $3471250 is to be levied upon a valuation of $571273600; what will be the rate to the hundredth of a mill? ARTICLE 209. Apportionment of Taxes. 1. $3400 is to be assessed upon a town; the valuation is $1269531.25, and 100 persons pay $1.50 each for poll tax ; find the rate of levy, and construct a table to $9000. With the above levy, find the tax to be paid by the follow- ing persons: 2. William Smith, property $7500, 2 polls. 3. G. W. Wright, property $5610, 1 poll. 4. Euth Williams, property $6495. 5. Seth Cooper, property $1698, 1 poll. 6. William Simpson, property $1627, 2 polls. 7. Enoch Ayres, property $1240, 3 polls. 8. Matthew Wilson, property $990, 1 poll. 9. The tax to be raised in a city is $4117136; the tax- able property is valued at $162580364 ; find the rate of levy to one thousandth of a mill, and construct a tax table to $90000. With the above table, find the amount of tax to be paid by : 10. Eli Wiggins, property $874. 11. Marion Thompson, property $194560. 12. Timothy Stewart, property $1418720. 13. Silas Burns, property $84. 14. John Shaw, property $848. 15. Jonas Newcome, property $8484. 16. Emmanuel Goldsmith, property $84848. R. T. E. 9. 130 KAY'S NEW TEST EXAMPLES. ARTICLE 211. Internal Revenue. 1. The tax on proof spirits is 70 cents a gallon; what would be the tax on a barrel of 48 gallons? 2. AVhat would be the tax on a barrel of whisky con- taining 52 gallons, 50^ above proof? 3. What would be the postage on a book weighing 1 Ib. 1\ oz., at the rate of 1 cent for each 2 ounces or frac- tion thereof? 4. What would be the postage on a letter weighing 1 Ib. 1\ oz., at the rate of 2 cents for every half ounce or fraction thereof? 5. What would be the postage on a package weighing 1 Ib. 7^ oz., at the rate of 1 cent for each ounce, or frac- tion thereof? 6. What would be the postage on 15 letters, each weighing \ oz. ? 7. What would be the postage on 15 packages, each weighing \ oz.? 8. What would be the postage on 15 books, sent sep- arately, each weighing \ oz.? 9. What would be the postage on 2 dozen books, each weighing 2 Ib.? 10. The tax on cigars is $3 per 1000; what must be paid for 216 boxes, containing 50 each? 11. The tax on small cigarettes is 50 cents per 1000; what will be the tax on 100 bundles, containing 200 small cigarettes each? 12. What will be the tax on 3 T. 13 cwt. of snuff, at 8 cents a pound? 13. A firm paid $30 postage on 2-oz. letters; how many were sent? 14. Paid $30 postage on 8-oz. books; how many were sent ? TAXES. 131 ARTICLE 212. Duties or Customs. 1. What is the duty on 5 T. 3 cwt. of flour sulphur, at $20 per ton? 2. What is the duty on 23040 steel pens, at 12 ct. a gross? 3. Find the duty on 100^000 Ib. of iron ore, at 75 ct. per ton. 4. Find the duty on 72000 shingles, at 35 ct. per 1000. 5. A cask of borax weighs 572 Ib. ; allowing 6% for tare, what will be the duty at 5 ct. per Ib.? 6. Imported an invoice of silk, costing $3739.30 ; what was the duty at 50^ ? 7. Imported 450 boxes raisins: gross weight of each, 25 Ib., tare 8% ; find the duty at 2 ct, per Ib. 8. What will be the duty on 2 dozen repeating rifles, costing in England 5 5 s. each, the duty being 25%, and the pound quoted at $4.88? 9. Find the duty on 46 T. Bessemer steel, at 45%; cost per ton, 6 10 s., and the pound being $4.84. 10. Imported 10 cases woolen cloths, weighing 272 Ib. each; tare, 5% ; cost, 90 ct. per Ib. What is the duty, at 35 ct. per Ib. and 40% ad valorem? 11. Find the duty on 72 crates of queensware costing 73 6 s. 8 d. per crate, commission 3^%, duty 55%, the pound =. $4.86. 12. Imported 100 cases German toys, costing 180 marks per case, commission 31% ; find the duty at 35%, the mark being 23.6 ct. 13. Bought 100 dozen umbrellas at 3 6 s. per dozen; what was the duty at 50%, 1 = $4.868? 14. Bought 18 bales Turkey sponge, weighing 130 Ib. each, at 5 s. 4 d. a Ib. ; find the duty at 20%, 1 =$4.86. 132 RAY'S NEW TEST EXAMPLES. RATIO. ARTICLE 214. What is the ratio of: 1. 140 to 7? 10. 1000 to 2. 37| to 3f? 11. 88! to 19f? 3. 56 to 2|? 12. 87 to 23? 4. 100 to 17? 13. 41f to 6f ? 5. 112 to 17!? 14. 7 to 175? 6. 18 to 171? 15. f to 18? 7. 18f to 7!? 16. $ to 100? 8. 40f to 25|? 17 42 to - 07? 9. 7f to 26? 18. 13^- to 4.5? 19. 9 A. to 18 sq. rd.? 20. 7 mi. 10 rd. to 30 rd.? 21. 1 bu. 1 pk. 1 qt. to 1 qt, 1 pt.? 22. 5 Ib. 4 oz. to 7 cwt.? 23. 3 weeks to 9 hr.? 24. 4 sq. mi. to 13 A.? ARTICLE 215. Find the antecedent in the following : 1. Consequent, 35; ratio, 20. 2. Consequent, 280; ratio, 100. 3. Consequent, 17!; ratio, 19. 4. Consequent, -|; ratio, ^. 5. Consequent, 8|; ratio, 6^. 6. Consequent, 3|; ratio, 4.6. 7. Consequent, 4.3; ratio, 6^. 8. Consequent, 15 sq. mi. ; ratio, .008. 9. Consequent, 2 ft. 9 in. ; ratio, 4|. 10. Consequent, 3 wk. 3 da. 12 hr. ; ratio, KATIO. 133 ARTICLE 216. Find the consequent in the following : 1. Antecedent, 137.2; ratio, 7. 2. Antecedent, 3.4; ratio, .08. 3. Antecedent, 4; ratio, 6-|. 4. Antecedent, f ; ratio, -^. 5. Antecedent, 4 bu. 1 qt. ; ratio, 6. 6. Antecedent, 13 gal. 3 qt. ; ratio, .05. 7. Antecedent, 14 hr. 40 min. ; ratio, 30. 8. Antecedent, 13.2 liters; ratio, .08. ARTICLE 217. Find the value of the following compound ratios : 1. 3. 4. 16 bu. 175 A. (27 (77 28 bu. 180 A. 27 da. : 22 da. horses : 63 horses. 5. 6. 7. 8. 1.2 : .3. 3 i : i ( 1 wk. : 8 hr. 1 16 men : 2 men. ( 6.4 : 8. < 4.5 : 9. I 396 : 7.2. ;6 men : 2 men. 8 da. : 16 da. 12yd. : 2yd. ARTICLE 219. Reduction of Ratios. Reduce the following ratios to their lowest terms : 1. 80 2. 259 3. 77 4. 999 5. 9999 6. 648 64. 111. 33. 99. 4545 486. 7. 388 : 1261. 8. 329 : 517. 9. 48 da. : 36 da. 10. 9 wk. : 2 da. 1 hr. 11. 22gal.:lgal.:lqt.:lpt. 12. 8 oz. : 3 Ib. Av. 134 KAY'S NEW TEST EXAMPLES. ARTICLE 220. Clearing Ratios of Fractions. Clear the following ratios of fractions : 1. 71 : 4f. 3. 6f : 2f. 2. 16f : 2. 4. 4| : 3f Express the following ratios in their simplest forms : 5. 5 6. 7, 16f : 8. 1 : PROPORTION. ARTICLE 223. To find Missing Terms. 1. 9 : 12 : : 51 : what? 2. 12 : 16 : : what : 28? 3. 38 : what : : 57 : 12? 4. 36 : what : : 27 : 72? 5. 27^ : 37| : : what : 18f ? 6. 8 : 9 : : 73 : what? 7. 8 : 9 : : what : 73? 8. 8 : what : : 9 : 73? 9. What : 8 : : 9 : 73? 10. 5 qt. : 2 pk. 2 qt. : : 24 : what? ^ 4 ! 4 'I } : 14. " 'yi': what : 3 cwt. 1 lb.? PROPORTION. 135 ARTICLE 224. Simple Proportion. 1. If 17 A. cost $205, what will 85 A. cost? 2. If 46 bu. of wheat cost $37.20, what will 115 bu. cost ? 3. If $1000 will buy 160 hogs, what will 1000 hogs cost? 4. What cost 210 brooms, at $2.60 per doz.? 5. Seventy horses cost $11000; at that rate, how many can be bought for $16500? 6. If a lot 46 feet front is worth $975, what would a lot 207 feet front be worth? 7. If 49 yd. of silk cost $50.40, what will 126 yd. cost? 8. If 27 gal. of wine cost $31.50, what will 84 gal. cost? 9. If a telegram of 40 words costs $1.70, what should be paid for a telegram of 76 words for the same distance? 10. If 15 dozen brooms cost $41.40, what will 800 brooms cost? 11. If $47 will buy 1750 Ib. of iron, what will 2450 Ib. cost? 12. If a car travels 506 mi. in 44 hr., how long would it require to go 1587 mi.? 13. A man has corn to feed 54 horses 38 weeks ; how long would it last 57 horses? 14. A laborer works for $1.25 a day, and is paid in potatoes at 55 ct. a bu. ; how many bushels will he re- ceive for 50 days work? 15. Ten pipes fill a reservoir in 64 hr. ; if 2 pipes were closed, how long would it take the others to fill it? 16. A man walks | mi. in ^- hr. ; how far can he walk in 44 da.? o o 17. If a gallon of brandy costs as much as 1 gal. 2 qt. of wine, how much brandy should be given for 1 gal. of wine ? 136 RAY'S NEW TEST EXAMPLES. 18. A watch loses 1 rain. 24 sec. in a week; how much will it lose in 4 da. 12 hr.? 19. If 2 T. 5 cwt. of hay cost $25.20, how much can be bought for $84? 20. A crew of 96 men have provisions for 72 days; how many men must desert, that the remainder may have enough for 108 days? 21. A man borrows 256 bu. of oats, worth 35 ct. a bu. ; how much should he return, the price having fallen 3 ct. a bu.? 22. How many bu. of oats, at 53 ct., should be given for 940 bu. 3 pk. of wheat, at 71 ct. ? 23. When flour is $10 a bl. the 10 ct. loaf weighs 1 Ib. 12 oz. ; what should it weigh when flour is $8 a bl.? 24. A man makes 5800 steps, of 33 in. each ; if his son's steps are 4 in. shorter, how many steps must he make in walking the distance with his father? 25. If a locomotive burns 200 bu. 1 pk. of coal in run- ning 441 mi., how far can it run with 227 bu. 1 pk.? 26. If a man can cut 12 C. of wood in 55 hr., how much can he cut in 22 days, working 10 hr. a day? 27. If 580 sheep can graze on 72 A. 80 sq. rd. of pasture, how much will be required for 850 sheep? 28. If a yard-stick casts a shadow 4 ft. long, when held upright, how high is the tree whose shadow is 220 ft. long? 29. Bought 120 chairs, at 70 ct. apiece; had the cost been 10 ct. more apiece, how many could I have bought? 30. Had the cost been 10 ct. less apiece, how many could I have bought? 31. Had I bought 30 more for the same money, what would each have cost? 32. Had I bought 20 less for the same money, what would each have cost? PROPORTION. 137 33. If a man earns $402 in f of a year, how much can he earn in of a year? 34. What cost 37-J- yd. of cloth, if yd. is worth $f ? 35. How long should I lend a man $880, to compensate for a loan of $660 for 60 days? 36. If .68 yd. of cloth is worth $1.16, find the value of .85 yd. 37. If the composition for a book of 336 pages cost $450.52, what will be the cost of composition for a sim- ilar book of 504 pages? 38. If a hog weighing 325 Ib. is worth $23.40, what should be given for one weighing 425 Ib.? 39. How many men can do in 5^- days as much work as 364 men can do in 8^ da,? 40. What sum will pay freight on 6 T. 15 cwt, as far as 3 cwt. 25 Ib. can be carried for $1.04? 41. A man was charged $132 for silk, but discovered that it had been measured with a measure 34 inches long, instead of 1 yd.; what was the true bill? 42. Eight cu. ft. of water weigh 5 cwt. ; what will be the capacity of a vessel containing 4 T. 7 cwt. 50 Ib. of water? 43. A grocer's weights are deficient at the rate of 1 oz. in 2 Ib. ; what is the true weight of a parcel sold for 240 Ib.? 44. At 10 ct. a Ib. (false), what will he charge for sugar, the true weight of which is 155 Ib. ? 45. If | make 160 pills, how many can be made from 3g29? 46. A town of 4750 inhabitants increased in population 950 in one year; at the same rate, what will be the in- crease the next year? 47. If I sell my horses at a gain of 36%, I clear $4560; what will be my profit if I sell at 63^ gain? 138 RAY'S NEW TEST EXAMPLES. 48. If muslin 27^ in. wide is worth 11 ct. a yd., how much should be paid per yd. for muslin 4 ft. 2^ in. wide? 49. If a school with 750 pupils sends 80 to the high school, how many should a school of 1800 pupils send? 50. The fore wheel of a wagon is 17 ft. 6 in. in circum- ference; and the hind wheel, 20 ft. 5 in.; how many revolutions will the fore wheel make while the hind wheel makes 756? 51. How many revolutions will the hind wheel make while the fore wheel makes 756? 52. A mining company employed 580 miners, the weekly pay-roll of wages being $630.75 ; what would be the weekly wages after 40 , men were discharged? 53. A man measuring a road gave the length at 840 yards, the true length being 825 yards ; how much too short was his yard-stick? 54. A clock loses 1 min. 12 sec. in 48 hr. ; how much will it lose in 6 da. 8 hr.? 55. A steamer goes 13 mi. 240 rd. per hour; a sailing vessel, 71 mi. per hour; how long will the latter be on a voyage which the steamer could perform in 73 hr. 12 min.? 56. If a county, having 350000 inhabitants, is entitled to 8 representatives, how many should be sent by a county whose population is 787500? 57. A man, whose farm is valued at $7930, is taxed $14.78 for a bridge ; what will be levied upon his neighbor, whose farm is valued at $8947? 58. With a certain machine a power of 90 pounds can move a weight of 3 T. 6 cwt. ; what weight can be moved by a power of 3 cwt. applied to the machine? 59. My gain on $4760 sales was $116.38; at the same rate, what will be my gain on $15928 sales? PROPORTION. 139 ARTICLE 225. Compound Proportion. 1. If 5 men in 6 da. earn $49.50, how much can 8 men earn in 9 da.? 2. If 6 men in 8 da. earn $78, how many men can be hired for 4 da. for $117? 3. If 8 men in 12 da. earn $120, how long can 14 men be hired for $210? 4. Twelve lots, each 15 rd. long and 12 rd. wide, cost $2400 ; at the same rate, what would be the price of 18 lots, each 12 rd. long and 10 rd. wide? 5. How many lots, 15 rd. by 7 rd., could be bought for $2800? 6. If lots are 9 rd. wide, how long should they be so that 22 lots should be worth $3960? 7. How wide must the lots be, so that 15, each 15 rd. long, may be worth $2700? 8. Interest for 6 mo. 10 da., at 6%, was $72.20; what would it have been for 3 mo. 24 da., at 8%? 9. A man bought 18 cows with his commission on $21600 sales, at %\% ; how many could he buy with the commission on $44000 sales at 1|%? 10. If 20 bu. of potatoes can be raised on a lot 20 yd. long and 20 yd. wide, how many bushels can be raised on another lot 10 rd. long and 10 rd. wide? 11. If a railroad carries 4500 pounds 1800 miles for $27, how far can 3000 pounds be carried for $11? 12. If 4000 books, of 384 pages each, require 200 reams of paper, how many similar books, of 324 pages each, can be printed from 216 reams of paper? 13. If 9 dogs catch 9 rabbits in 9 min., how many rab- bits will 12 dogs catch in 12 min.? 14. If 10 cats catch 10 rats in 10 min., how many cats must be employed to catch 18 rats in 18 min.? 140 RAY'S NEW TEST EXAMPLES. 15. If a merchant's profits are $7380 for 9 mo., when he is clearing 8^ a year, what will be his gain for 7 mo., when he is clearing 10% a year? 16. If the 10 ct. loaf weigh 2 Ib. 3 oz., when flour is $9.75 per barrel, what should the 8 ct. loaf weigh, when flour is $6.50 per barrel? 17. If carpets cost $810 for a house of 12 rooms, each 15 b}~ 18 feet, what will the same kind of carpet cost for a house of 10 rooms, each 12 by 15 feet? 18. What is the ratio of the glazing of two houses: the first contains 15 rooms, with four windows each; each window has 2 sashes; each sash, 6 panes, 11 by 16 in.; the second house has 11 rooms ; each room, 3 windows ; each window, 2 sashes; each sash, 2 panes, 15 by 32 in.? 19. A farmer sold his potatoes for $147.84 ; the next year he planted a strip which was longer in the ratio of 5 to 4, but narrower in the ratio of 3 to 4 ; crops were more abundant in the ratio of 10 to 9, and prices \vere lower in the ratio of 7 to 8; what should he receive for his crop the second year? 20. A road 300 rd. long and 40 ft. wide, was dug 2 ft. 6 in. deep by 40 men in 5 days, of 10 hr. each ; how many men must be employed to make a road 5 mi. long, 2 rd. wide, dug 3 ft. deep, in 16 days, of 11 hr. each? 21. If the freight of 20 hogsheads of sugar, each weighing 13 cwt. 20 Ib., is $44.88 for 65 miles, what should be the freight on 250 barrels of sugar, each weigh- ing 2 cwt. 8 Ib., for 66 mi.? 22. If a floor 33 ft. 9 in. by 26 ft. 8 in. cost $22.50, what will be the cost of a floor 39 ft. 6 in. by 29 ft. 4 in.? 23. How many flag-stones, each 88 in. long and 20 in. wide, will be required to replace a pavement containing 8800 bricks, each 8 in. long and 4 in. wide? PROPORTION. 141 24. If 5 men can dig a cellar 48 ft. long, 20 ft. wide, and 9 ft. deep, in 8 da., of 8 hr. each, how many men must be employed to dig a cellar 60 ft. long, 27 ft. wide, and 10 ft. deep, in 10 days, of 10 hr. each? 25. If an engine, running 18 mi. 240 rd. in 40 min., can carry a train from one station to the next in 2 hr. 27 min., how long would the same distance take a freight train moving 8 mi. 240 rd. in 1 hr. 40 min.? 26. If the interest of a certain sum for 3 yr. 6 mo., at 6%, is $266.70, what will be the interest of a sum | as large, for 6 yr. 3 mo., at 10%? 27. A certain excavation costs $75. What would be the cost of an excavation 20% wider, 25^ deeper, and 50% longer? ARTICLE 226. Partnership. 1. Two partners put in $7500 and $4500 ; they lose $1500; how should this loss be apportioned? 2. A's capital was $850; B's, $750. At the end of one year they have $2000; how should it be divided? 3. A contributes $90; B, $80; C, $130; they lose $210; what is the loss of each? 4. Divide 3948 into 2 parts, which shall be to each other as 3 to 4. 5. Divide 3948 into 2 parts, which shall be to each other as 1 to \. 6. Divide 3948 into 3 parts, which shall be to each other as 3, 4, and 5. 7. Divide 3948 into 3 parts, which shall be to each other as ^, ^, and \. 8. Divide 19.56 into 2 parts, which shall be to each other as 7.9 and 8.4. 9. Divide 3.925 into 2 parts, which shall be to each other as 28 and -%. 142 RAY'S NEW TEST EXAMPLES. 10. A has 60 A. 120 sq. rd. ; B, 81 A. They join these for a pasture, for use of which they receive $75.60; how should this be divided? 11. A father left his three sons the following sums: $750, $675, and $375; but his property amounts to only $1440; how should this be divided? 12. A society of 55 musicians charter a ear for $44, to carry them to Columbus. If they receive a second society of 33 to go with them, how should the expense be divided? 13. A's lot is 80 ft. front; B's, 75 ft,; C's, 100 ft.; D's, 55 ft. ; and E's, 85 ft. How much should each contribute, to raise $50, to pay for watering the street? ARTICLE 227. Bankruptcy. 1. A bankrupt owes $46000; his property sells for $20470, and the expenses are $1150 ; how much will he pay on the dollar? 2. A bankrupt's assets are $16800, his liabilities are $55000, and the expenses of settlement are $2500; how much will he pay on the dollar? 3. A speculator fails, owing $250000; the assignee sells his real estate for $23000, and his personal property for $18000, and charges $3500 for fees and expenses; what will a creditor receive for a claim of $940 ? ARTICLE 228. General Average. 1. A ship is valued at $63000; and its cargo, at $32000; what will be the general average on a loss of $1140? 2. A shipped 300 barrels of flour; B, 240; and C, 100 barrels ; 160 barrels were lost in a storm. How nuK'h of this loss will fall on each? PROPORTION. 143 3. Goods valued at $800 were thrown overboard from a ship valued as $10000, with a cargo valued at $15600: how much will A lose, his shipment being valued at $800? 4. A ship is valued at $40000; and the cargo, at $35600. During a storm, A's shipment, valued at $1890, is washed overboard; how much will he receive for it? ARTICLE 229. Partnership with Time. 1. A invested $400 for 4 mo. ; B, $600 for 6 mo. ; how should they divide the $780 gained? 2. A and B were to receive $152.10 for removing a bank of earth. A furnished 10 carts 8 days; and B, 12 carts 6 days. How much should each receive? 3. A arid B each put in $1000 at the beginning of the year, but at the end of 6 mo. A took out $500; they gained $2310 during the year. How should it be divided? 4. A put in $500 for 4 mo.; B, $600 for 3 mo.; C, $250 for 4 mo.; they lose $576. What will be the loss of each? 5. A and B were in partnership 4 mo. A had $2000 in the whole time; B put in $1000 at the beginning of each month ; the gain was $414. How should it be divided? 6. A pastured 30 cows 7 mo. ; B, 50 cows 9 mo. ; the expense was $217.80; How should it be divided? 7. A commenced business with $3000 ; 6 months after, B joined him with $3600 ; 4 years from commencement, they had gained $4305. What was the share of each? 8. A and B were partners for 10 mo. A put in $700 at first, and two months afterward $200 more ; B put in $500 at first, and three months afterward $500 more. A's loss was $215 ; what was B's loss? 144 KAY'S NEW TEST EXAMPLES. ARTICLE 230. Equation of Payments. Find the average time in the following : 1. $600, due in 3 mo.; $400, in 5 mo.; and $500, due in 2 mo. 2. $750, in 3 mo. ; $750, in 5 mo. ; and $750, in 7 mo. 3. $30, in 8 mo. ; $20, in 4 mo. ; and $40, in 10 mo. 4. $60, due now; $60, in 3 mo.; and $60, in 9 mo. 5. $700, due now ; $500, in 10 da.; and $700, in 20 da. 6. $60, due in 60 da. ; $90, in 90 da. ; and $60, due in 120 da. 7. $200, due in 4 da.; and $5000, due in 30 da. 8. $70, due in 7 da.; $80, due in 8 da.; and $90, in 9 da. 9. Bought goods as follows: May 7, $10 ; May 9, $15; May 20, $34. Find the equated time. 10. Bought $420 worth of goods: 1 seventh cash, 2 sevenths in 7 mo., balance in 14 mo. Find the equated time 11. Bought the following bills: July 17, $300; Aug. 26, $700. Find the equated time. 12. Bought: April 13, $400; May 1, $550; May 7, $350 ; May 14, $700. Find the equated time. 13. Bought: Aug. 7, $300; Aug. 28, $900; Sept. 7, $900; Sept. 28, $300. Find the equated time. 14. Bought: March 5, $500; April 1, $400; April 14, $200; May 1, $600. Find the equated time. 15. $700 was due Jan. 1 ; $900, May 1 ; and $400, July 1. Find the equated time. 16. Bought goods as follows: May 19, 1884, at 6 mo., $1360; June 12, 1884, at 4 mo., $2168; July 25, 1884, at 6 mo., $988; Aug. 3, 1884, at 4 mo., $1650. Find the equated time. PROPORTION. 145 ARTICLE 232. Average. Find the average of the following : 1. 15 Ib. of sugar, at 9 ct. a Ib. ; and 10 lb., at 14 ct. a lb. 2. 10 oz. of gold, at $18^- an oz. ; and 20 oz. of silver, at 1)5 ct. an oz. 3. 15 lb. of honey, at $.40 a lb.; and 10 lb. of sugar, at 5 ct. a lb. 4. 30 gal. of wine, at $2.22 a gal., diluted with 7 gal. of water. 5. 7 gal. of alcohol, at $2.40 a gal. ; 2 qt. of whisky, at 15 ct. a qt. ; and 2 gal. of water. 6. A man walked 2 mi. in 20 min.35 sec., and then 4^ mi. in 40 min. 30 sec. ; find the average time for 1 mile. 7. The barometer, at 5 observations, stood 29.81 in., 29.87 in., 29.83 in., 29.91 in., and 29.93 in.; what was the average height? 8. In a regiment, 230 men averaged 5 ft. 4 in. ; 280 averaged 5 ft. 8 in. ; and 205 averaged 5 ft. 9 in. What was the average height? 9. A steamer went 13 mi. 160 rd. per hour, for 7 hr. ; and then 12 mi. 30 rd. per hour, for 11 hr. What was the average speed? 10. 13 members of a council were present at 11 meet- ings, 2 at 12, 2 at 14, and 3 at 15 ; what was the average number of meetings attended by each of the 20 mem- bers? 11. What was the average number of members presen at each of the 15 meetings? 12. In a dwelling, 3 floors are each 15 by 17 ft.; 3 are 14 by 18 ft. ; and 3 are 19 by 24 ft. What is the average surface ? R. T. E. 10. 146 KAY'S NEW TEST EXAMPLES. INVOLUTION. ARTICLE 234. Find the following : 1. Second power of 81. 2. Third power of 32. 3. Fourth power of 25. 4. Fifth power of 3.1. 5. Second power of 69.3. Find the square of: 11. 309. 12. 54.03. 13. 60f. Find the cube of: 20. 36. 21. 125. 22. 105. 14. if 15. lif 16. 151 23. 13|. 24. 19.1. 25. 347. 6. Third power of 5.5. 7. Fourth power of 61. 8. Third power of 16 T V 9. Second power of 991. 10. Sixth power of l\. 17. 30. 18. 6 3 V 19. 44^. 26. . 27. 10.4. 28. 10. Find the fourth power of: 29. 91. 30. 6.2. 31. 101 32. 331 33. 8.4. 34. 28. Find the fifth power of: 38. 11.1. | 39. 27f. Reduce the following : 41. 223. 42. 16.52. 43. (17*)*. 44. 19.1 s . 35. if- 36. 151 37. 3f 40. 105. 45. 46. EVOLUTION. 147 EVOLUTION. ARTICLE 238. Square Root. Find the square root of : 1. 144. 2. 1444. 10. 1.21. 11. 15.21. 19. 50^. 20. 8 ? -. 3 7744. 12. 10609. 21. 12f 4. 625. 13. 9409. 22. 1000. 5. 5625. 6. 15625. 14. 576. 15. 5476. 23. 54, 24. 16.1. 7. 30625. 8. 50625. 9. 180625. 16. 96^. 17. 215f 18. 1235^- 25. 257. 26. 25.7. 27. 12.09. ARTICLE 239. Square Root by Factoring. Find, by factoring, the square root of: 1. 1225. 2. 2304. 3. 4096. 4. 11025. 5. 5184. 6. 18225. 7. 50 X 450. 8. 125 X H25. 9. 125.44. ARTICLE 240. Applications of Square Root. 1. The base of a right-angled triangle is 60; perpen- dicular, 45 ; find the hypotenuse. 2. The hypotenuse is 41 ft. ; the base, 40 ft. ; find the perpendicular. 3. A ladder 53 ft. long reaches a window 45 ft. from the ground ; how far is the foot of the ladder from the bottom of the wall? 4. A well is 63 ft. deep and 16 ft. wide ; what is the length of the longest pole that can be placed entirely within the well? 148 KAY'S NEW TEST EXAMPLES. 5. A mast, 77 ft. high, stands in the middle of ship 72 ft. wide ; how long is the rope ladder from the ship's side to the mast-head? 6. A tree, 72 ft. high, is broken 20 ft. from the ground; how far from the foot will the top reach? 7. A pole, 45 ft. high, stands in the center of a circular ring 56 ft. in diameter; what is the length of the rope from the top of the pole to the edge of the ring? 8. A rope, 73 ft. long, reaches from the edge of a ring to the top of a center pole 55 ft. high ; how wide is the ring? 9. Base and perpendicular each 60 ft.; how long is the hypotenuse? 10. If the hands of a clock were 3 in. and 4 in. long, how far apart would the points be at 3 o'clock? 11. A boy is due south from his home 144 mi.; he travels due west 165 mf. ; how far is he then from home? 12. A stream is 120 feet wide ; how long must a bridge b, if it rises in the center 11 feet above its height at the end piers? 13. Hypotenuse, 80 ft.; base and perpendicular equal; find them. 14. A is 60 mi. north of B, and 70 mi. west of C ; how far apart are B and C? 15. If Cleveland is 225 mi. further north than Cincin- nati, and 120 mi. further east, how far apart are the two cities? ARTICLE 241. 1. A square farm contains 360 A. ; how long is it? 2. A field is 12 rd. square ; what is the side of another square field containing 1 sq. rd. more than twice as much as the first? EVOLUTION. 149 3. A farmer has a field 87 rd. square, which he ex- changed even with his neighbor for two square fields, one 63 rd. long; how long was the other? 4. How much more fence will be required for a field 80 rd. long and 20 rd. wide, than for a square field of equal area? 5. Find the side of a square field equal to 4 fields 5 rd., 12 rd., 84 rd., and 3612 rd. square. 6. There are 3 square fields: the first is 120 rd. sq.; the second contains 3^ ; and the third, 5^ as much land as the first. What is the difference in the length of the two latter fields? ARTICLE 244. Cube Root. Find the cube root of: 1. 13824. 2. 79507. 3. 250047. 4. 405224. 13. 3. 14. 300. 15. .009663597. 16. .000002146689. 17. 5. 314432. 6. 59319. 7. 8615125. 8. 135005697. 18. .4. 19. .04. 20. .004. 21. 592 T 8 , 22. f . 9. 746142643. 10. 620650.477. 11. 282.300411). 12. .030664297. ARTICLE 245. 1. What is the side of a cubical box which contains 7 cu. ft. 71 cu. in.? 2. What is the side of a cubical tank which contains 2744 cu. ft.? 3. How many cubical blocks, 3 in. long, can be cut from a cubical block 15 in. long? 150 RAY'S NEW TEST EXAMPLES. 4. How many cubical blocks, ^ in. long, can be cut from a cubical block 15 in. long? 5. What is the side of a cube which weighs 12-|-% as much as a cube 11 in. in diameter? 6. What is the side of a cube which contains 2 cu. ft.? MENSURATION. ARTICLE 247. Areas of Parallelograms. Find the surface of: 1. A pavement, 20 yd. long and 6 ft. 9 in. wide. 2. A meadow, f mi. long and 40 rd. wide. 3. A floor, 18 ft. 9 in. long and 13 ft. 4 in. wide. 4. A canal, 45 mi. long and 30 ft. 3 in. wide. 5. A park, 990 ft. by 440 ft. 6. A pasture, 20 ch. by 16 ch. 7. A wall, 8 ft. high and 30 yd. long. 8. A canvas, 5.4 in. by 7.5 m. 9. A roof, each side being 16 ft. 6 in. by 40 ft. 10. A street, 2 mi. 240 rd. long and 66 ft, wide. 11. How many bricks, 4 in. by 8 in., will be required for a pavement 40 ft. by 8 ft.? 12. How many acres in a field 120 rd. square? 13. How many yards of carpet, f yd. wide, will be re- quired for a floor 15 by 18 ft. ? 14. A floor, 16 ft. long, requires 24 sq. yd. of carpet ; how wide is the floor? 15. A man has a lot 54 yd. long and 24 yd. wide, which he exchanged for a square lot of equal surface ; how much more fence would the first lot require than the last? MENSURATION. 151 ARTICLE 248. Area of Trapezoid. 1. A sky-light is 20 ft, long, and the two ends are 17 ft. and 10 ft. wide ; what is the surface? 2. Find the surface of a field in the form of a trape- zoid, the parallel sides being 73 rd. and 35 rd., and lying 32 rd. apart. 3. A lot is bounded by four streets: two of these are parallel, and measure 70 ft. and 90 ft. along the lot, and are 135 ft. apart; what is the surface of the lot? ARTICLE 249. Area of Triangles. Find the area of: 1. A triangle, 40 ft. long and 20 ft. high. 2. A triangle, 96 yd. long and 55 ft. high. 3. A triangle, 10 ft. 8 in. long and 6 ft. 9 in. high. Find the area of a right-angled triangle: 4. The base, 80 ft. ; perpendicular, 60 ft. 5. The base, 60 ft; perpendicular, 80 ft. 6. The base, 88 rd. ; perpendicular, 25 rd. Find the area of the following triangles : 7. The sides are 51 yd., 68 yd., and 85 yd. 8. The sides are 51 yd., 52 yd., and 53 yd. 9. The sides are 52 rd., 56 rd., and 60 rd. ARTICLE 250. Area of Trapezia. 1. Find the area of a trapezium, one diagonal being 120 rd., and the perpendiculars to the diagonal from the opposite angles being 45 rd. and 55 rd. 2. Diagonal measures 70 ft., and the two perpendicu- lars on the diagonal, 30 ft. and 40 ft.; find the area of the trapezium. 152 RAY'S NEW TEST EXAMPLES. 3. A man has a four-sided lot: the line between two opposite corners is 132 ft. long, and the other corners are 88 ft. and 110 ft. perpendicularly distant from that line ; find the area. 4. Diagonal, 100 rd. ; perpendiculars on it from opposite corners, 50 rd. and 70 rd. ; find the value of the trapezium, at $960 per acre. ARTICLE 251. Diameter and Circumference of a Circle. 1. Diameter, 20 ft. ; find the circumference. 2. Circumference, 20 ft. ; find the diameter. 3. Radius, 26 ft. ; find the circumference. 4. The diameter of a circular plat is 90 feet ; what is the length of the fence around it? 5. What is the thickness of a tree, if it measures 4 ft. 8 in. around? 6. What is the distance across a circular field, if it is 170 rd. around it? 7. What is the distance around a circular field, if it is 170 rd. across it? 8. What length of tyre would be required for the wheels of a wagon, the front ones being 5 ft. 4 in. in diameter, and the hind ones 5 ft. 11 in. in diameter? ARTICLE 252. Area of a Circle. Find the area of: 1. A circle whose radius is 25 ft. 2. A circle whose diameter is 20 ft. 10 in. 3. A circle whose diameter is 3^ in. 4. A man lays out a lawn with a rope 60 ft. long, fastened to a stake at the center ; how much land in the lawn ? MENSURATION. 153 5. What is the diameter of a circle that is equal to a square whose side is 30 ft.? 6. What is the side of a square that is equal to a circle whose diameter is 30 ft.? 7. A lot, 120 feet in diameter, has a gravel walk 20 feet wide just within its circumference ; what is the sur- face of the grass plat inside the gravel walk? 8. A lot, 18 rd. in diameter, has around its center a grass plat 12 rd. in diameter ; what is the area of the paved ring covering the rest of the lot? MENSURATION OF SOLIDS. ARTICLE 254. Surface of Prism or Cylinder. 1. Find the surface of a right prism 16 ft. high, standing on a triangular base whose sides are 6 ft., 8 ft., and 10 ft. 2. Find the surface of a rectangular prism 4 ft. high, standing on a base 2 ft. square. 3. Find the surface of a rectangular prism 2 ft. high, standing on a base 4 ft. square. 4. Find the entire surface of a cylinder 10 ft. high and 15 in. in diameter. 5. Find the convex surface of a cylinder 13 in. high, with a radius of 2 in. 6. Find the entire surface of a cylinder 13 ft. 2 in. high, and 6 ft. 6.54 in. in circumference. ARTICLE 255. Volume of Prism or Cylinder. 1. How many cu. in. in a prism 10 in. high, on a base 2 in. square? 2. How many cu. in. in a prism 2 in. high, on a base 10 in. square? 154 RAY'S NEW TEST EXAMPLES. 3. Find the volume of a flag-stone 10 ft. long, 3 ft. 9 in. wide, and 8 in. thick. 4. A sill is 40 ft. long and 9 in. wide ; how thick must it be to contain 25 cu. ft.? 5. Find the volume of a cylinder 20 in. high, whose circumference is 39.27 in. 6. A cylinder 10 in. in diameter contains 19G3^ cu. in.; what is its height? ARTICLE 256. Surface of Pyramid or Cone. 1. Find the convex surface of a right pyramid, the base being 18 in. square, and the slant height 4 ft. 2. Find the convex surface of a cone, the radius of the base being 6 in., and the slant height 8 in. 3. Find the entire surface of a cone, the diameter of the base being 20 in., and the slant height 40 in. 4. Find the entire surface of a cone, the diameter of the base being 40 in., and the slant height 20 in. ARTICLE 257. Volume of Pyramid or Cone. 1. Find the volume of a pyramid 48 ft. high, on a base 18 in. square. 2. The height of a pyramid is 8 ft., and the base is a triangle whose sides are 6, 8, and 10 in.; find the volume. 3. Find the volume of a cone whose altitude is 20 ft., and the diameter of the base 4 ft. 4. Find the volume of a cone, the altitude being 12 ft., and the radius of the base being 3 ft. 4 in. 5. i'he altitude of a cone is 2 ft., and the circumfer- ence of the base is 2 ft. ; find the volume. MENSURATION. 155 ARTICLE 258. Surface of a Sphere. Find the surface of: 1. A sphere whose diameter is 22 in. 2. A sphere whose radius is 4 ft. 3. A planet whose diameter is 2465 mi., supposing it to be a sphere. 4. If a base ball is 2-J- in. in diameter, how much leather will be required to cover 1600 balls, adding 10^ for waste? ARTICLE 259. Volume of a Sphere. Find the volume of : 1. A sphere 8 ft. 2 in. in diameter. 2. A globe whose radius is 20 in. 3. A planet whose diameter is 2240 miles, supposing it to be a sphere. 4. Find the weight of 500 cannon-balls, each 2 ft. in diameter, a cubic foot of iron weighing 430 Ib. ARTICLE 260. Applications of Mensuration. 1. What will it cost to sod a yard 40 ft, by 32 ft., at 11 ct. a sq. yd.? 2. A room is 18 ft. long, 15 ft. wide, and 10 ft. high: what will the plastering cost, at 5 ct. a sq. yd., deduct- ing 1 opening, 6 ft. square; 2 openings, 3 ft. 6 in. by 8 ft.; and 3 openings, 4 ft. by 7 ft. 6 in.? 3. What will it cost to paint both sides of a fence 78 ft. long and 5 ft, 6 in. high, at 14 ct. a sq. yd.? 4. A fish pond, 80 ft. in diameter, is surrounded by a tight fence 5 ft. 10^- in. high ; what will it cost to paint that fence, at 15 ct. a sq. yd.? 156 KAY'S NEW TEST EXAMPLES. 5. A museum room is 70 ft. long, 40 ft. wide, and 22 ft. high; what will it cost to paint the walls and ceiling at 29 ct. a sq. yd., deducting 1 sky-light, 14 ft. sq. ; 4 doors, 5 ft. 3 in. by 10 ft.; and 12 windows, 6 by 9 ft.? 6. What will it cost to plaster a concert hall 100 ft. long, 70 ft. wide, and 26 ft. high, at 22^ ct. a sq. yd.; deducting 8 openings, 8 by 12 ft., and 3 openings, 7 by 14 ft.? ARTICLE 261. Board Measure. 1. How many feet in an inch board 20 ft. long and 9 in. wide? 2. How many feet in a 3 in. plank 16 ft. long and 14 in. wide? 3. How many feet in a sill 30 ft. long, 10 in. wide, and 5 in. deep? 4. One sixth of the thickness being lost in sawing, how many feet of 2 in. plank can be made from a stick 2 ft. square and 20 ft. long? 5. One third of the thickness being lost in sawing, how many feet of -J- in. boards can be made from a stick 2 ft. square and 14 ft. long. (All boards less than 1 in. thick are counted and measured as if 1 in. in thickness.) 6. How many feet in a plank 2 in. thick, which is 18 ft. long, 16 in. wide at one end, and 10 in. wide at the other end ? ARTICLE 262. Masons' and Bricklayers' Work. 1, How many perches in a pile of stone 450 ft. long, 440 ft. wide, and 4 ft. high? 2. A cellar is 9 ft. deep, 39 ft. long, and 24 ft. wide inside : if the walls are 18 in. thick, how many perches of stone will they require? MENSURATION. 157 3. A cellar is 10 ft. deep, 48 ft. long, arid 19 ft. wide, measuring the outside ; the walls are 2 ft. thick ; what will the stone cost, at $4.12^ a perch? 4. A pile of stone is in the form of a cone, 45 ft. in diameter at the bottom, and 17 ft. high; what is it worth, at $1.75 a perch? 5. How many bricks in a wall 160 ft. long, 7 ft. high, and 2 ft. thick, allowing 20 bricks to 1 cu. ft. ? 6. The bricks in a wall are 9 in. by 4 in., and 2-J in. thick ; what will they cost, at $7.50 per 1000, the wall being 72 ft. long, 12 ft. 6 in. high, and 2 ft. 6 in. thick? ARTICLE 263. Measurement by Bushels or Gallons. 1. How many bushels in a bin 16 ft. long, 10 ft. 6 in. high, and 4 ft. 4 in. wide? 2. How many bushels in a crib 15 ft. square and 8 ft. high? 3. A pit is 10 ft. square and 28 in. deep ; how many bushels of potatoes w r ill it hold? 4. How many bushels of lime can be made in a kiln in the form of a cone, 14 ft. high, the diameter of the base being 11 ft. 8 in.? 5. How many bushels of barley can be put in a cylin- drical tub 16 ft. in diameter and 4 ft. deep? 6. How many gallons are equal in volume to 55 bu. ? 7. How many bushels are equal in volume to 1536 gal.? 8. How many gallons in a tank 7 ft. in diameter and 11 ft. deep? 9. How many barrels (31^- gal. each) in a reservoir 63 ft. square and 5 ft. 6 in. deep? 10. A cistern is made 8 ft. 4 in. in diameter and 11 ft. deep; what will it cost, at 80 ct. a barrel? 158 RAY'S NEW TEST EXAMPLES. PROGRESSIONS. ARTICLE 265. Arithmetical Progression. Case I. 1. The first term is 770; the common difference, 10; what would be the 20th term of an increasing series? 2. The first term is 770; the common difference, 10; what would be the 20th term of a decreasing series? 3. A new house rents for $900 per year ; if the rent is reduced $30 each year, what will be the rent the 15th year? 4. The houses on an avenue are numbered regularly, beginning with 720 ; what will be the number of the 63d house? 5. If lots, 20 ft. wide, are numbered in regular order along a line, how far will the 36th lot be from the start- ing point? 6. What is the 100th term of a decreasing series, the 1st term being .004, and the common difference .000004? ARTICLE 266. Case II. 1. The extremes are 7 and 70; the number of terms, 10 ; find the common difference. 2. The 1st term is 18; the 8th term, 900; find the common difference. 3. The extremes are 1 and 1000 ; the number of terms, 28 ; find the common difference. 4. If boys are paid according to their ages, and a boy 13 years old earns $3.70 a week, while a boy 19 years old earns $7.30 a week, how much is the increase for each year? 5. The 1st term is 721 ; the 12th term, 127; find the common difference. PROGRESSIONS. 159 ARTICLE 267. Case III. 1. The extremes are 4 and 80; the number of terms. 20 ; find the sum of the series. 2. A man earned $370 the first year, and his salary was regularly increased, so that in the 9th year he re- ceived $1130; what were his total earnings in 9 yr. ? 3. The extremes are 6 and 100, and the number of terms 10 ; find the sum of the series. 4. Extremes, 10 and 100; number of terms, 6; what is the sum of the series? 5. The 1st term is 450 ; common difference, 7 ; what is the sum of 10 terms of an increasing series? 6. The 1st term is 450; common difference, 7; what is the sum of 10 terms of a decreasing series? 7. The 15th term of an increasing series is 972; the common difference, 9; what is the sum of the 15 terms? 8. The 1st term is 11 ; the 8th term, 67; what is the sum of the series, there being 12 terms? ARTICLE 269. Geometrical Progression. Case I. 1. The 1st term of an increasing geometric series is 5; the ratio, 3; what is the fourth term? 2. The 1st term of an increasing geometric series is 3 ; the ratio, 5 ; find the fourth term. 3. The 1st term of a decreasing geometric series is 6 ; the ratio, 2 ; find the fifth term. 4. The 1st term of a decreasing geometric series is 2; the ratio, 6; what is the fifth term? 5. What is the 8th term of an increasing geometric series, the first term being 40, and the ratio 3? 160 RAY'S NEW TEST EXAMPLES. ARTICLE 270. Case II. 1. Find the sum of 10 terms of the series whose first term is 6, and ratio 2, the series being increasing. 2. Find the sum of 8 terms of the geometric series 3, 6, etc. 3. Find the sum of 8 terms of the geometric series 6, 2, etc. 4. Find the sum of the infinite decreasing series, of which the first term is f, and ratio . 5. Find the sum of the infinite geometric series 3, 2, etc. 6. Find the sum of the infinite geometric series, whose first term is .148, and ratio 1000. MISCELLANEOUS EXAMPLES. 1. Reduce -Jff-f-ff to its lowest terms. 2. What is 27%% of f ? 3. What is the value of the ratio, 2% pk. : 4 bu.? 4. What is the interest of $745.20 for 2 yr. 7 mo. 6 da., at 5%? 5. What cost 6 bu. 6 qt. of cherries, at 60 ct. a peck? 6. What is the equated time of the following: $750, in 34 da.; $800, in 40 da.; and $950 in 50 da.? 7. An agent sent the owner $804.20 for rent of house 28 months, retaining 5^ commission and $47 expenses ; what was the monthly rent? 8. How much would be received for 24 bu. 3 pk. of peaches, packed in baskets containing 2 pk. 6 qt. each, and sold at $1.70 per basket? 9. What will be the proceeds of a note of $475, dated May 29, 1860, at 90 da., and discounted in bank July 1, at 41^? 10. What will be the cost of a pile of wood 8.5 m. long, 6.8 m. wide, and 3.2 m. high, at 19 fr. per stere? 11. What cost 420 boards 16 ft. long, 9 in. wide, and 1 in. thick, at 31 ct. per ft.? 12. If 51 yd. cost $421, what will 81 yd. cost? 13. What cost 7707 Ib. of wheat, at $1.20 per bu.? 14. Find the convex surface of a cone whose slant height is 16 ft, and base 12 in. in diameter. 15. What is the present worth of a debt of $320, due in 7 yr., money being worth 4% ? R. T. E.-li. . (161) 031 v 1G2 KAY'S NEW TEST EXAMPLES. 16. A has 275 bu. wheat ; B, 405 bu. corn ; C, 205 bu. oats ; what would be the contents of the largest basket with which each one could exactly measure his grain? 17. A cistern is 4 ft. in diameter, and 3 ft. deep; what will it cost to line it with sheet lead weighing 5 Ib. to the square foot, and costing 13 ct. per Ib. ? 18. What would be the amount of $333.33, at interest 3 yr. 3 mo. 3 da., at 3^%? 19. What cost 7381 Ib. of hay, at $17.50 per ton? 20. I invested $16170 in bonds, at 5% premium, and sold at 8% premium ; find my gain. 21. In 14 meters, how many yards? 22. What principal, in 2 yr. 8 mo., at 7|%, will earn $69.68 interest? 23. At 7 ct. a yd., what will a strip of canvas cost, ex- tending along the four fences of a lot 42 rd. square? 24. Invested $23100 in bonds, at 5% premium, and sold at 5% advance; find my gain. 25. A invested $5400 for 7 mo.; B, $5600 for 9 mo.; they gained $546. Divide it. 26. Find the cost of a lot 100 rd. sq., at $100 per A. 27. Keduce , _!, 5 to fractions having the least 15 6 5 common denominator. 28. A debt of $420 will be due in 5 yr. ; what should be the discount for cash, if money is worth 4% ? 29. The first term of an increasing arithmetical pro- gression is 735 ; the common difference, 4^ ; find the 119th term. 30. Find the value of a cubical pile of wood 14 ft. long, at $2.40 a cord. 31. A vat is 11 ft. long, 7 ft. wide, and 9 in. deep; what is its capacity in gallons? 32. In 21 Ha. how many acres? MISCELLANEOUS EXAMPLES. 163 33. A man bought stock at 22^ discount, and sold it at 4% premium ; what / did he gain? 34. If 8 drivers receive $16.20 for trips, of 1 hr. 30 min. each, how much should 12 drivers receive for 10 trips, of 2 hr. each? 35. 18 is what % of 33? 36. Hcduco 11111111 sq. in. to A. 37. What is the square root of 5313025? 38. A fly-wheel is 10 ft. in diameter; what distance does a point in the circumference move in 16 revolu- tions? 39. After 22% of my flock died, I had 273 remaining; how many died? 40. How many bushels in a box 3 ft. long, 28 in. wide, and 16 in. deep? 41. How many minutes in the first four months of the year 1888? 42. Find the area of a triangle whose base is 4 rd., and height 4 yd. 43. What cost 1040 pwt. of silver, worth 91 J ct. per oz.? 44. If a sidewalk, 1 mi. 120 ft. long, cost $487.60, what will one 90 rd. long cost? 45. A note for $940, dated Jan. 23, payable in 3 months, was discounted in bank March 20, at 5% ; what was the discount? 46. What cost 56 three-inch planks, 30 ft. long and 12 in. wide, at 2 ct. per foot? 47. What is the least quantity of iron that would make an exact number of 25 Ib. balls, or 30 Ib. plates, or 35 Ib. bars, without remainder in either case? 48. What debt, due in 6 years, is now worth $375, money being worth 5%? 49. What % would be lost by buying an article above its value, and selling it 10% below its value? 164 RAY'S NEW TEST EXAMPLES. 50. In 50 kilograms how many pounds? 51. AVhat would be the compound interest of $300 for 4 yr, at &% ? 52. How many bushels of cranberries can be bought for $39.90, at 10 ct. 5 m. a pt.? 53. A foundry building and patterns are valued at $18000; what would be the premium for insuring f of this value, at \\%1 54. Find the side of a cubical box that will hold as much as another box 80 in. long, 75 in. wide, and 1 yd. high (inside measures). 55. What cost 49.3 meters of broadcloth, at 17 francs per meter? 56. A steamer is worth $105000, and a man sells f of his interest for $14700 ; what part of the ship did he own? 57. A man gained 5% the first year, and 8% the second year, at the end of which he was worth $15876; what capital had he at first? 58. How many hours per day must 42 men work, for 8 da., to do as much as 56 men can do in 6 da., of 9 hr. each? 59. A debt having run 4 yr. 6 mo., at 8%, the interest was $44.10; what was the amount? 60. What cost 7000 qt. bags of salt, at 36 ct. a bu.? 61. At 16| ct. per doz., how many lemons can I buy for $50? 62. How many bushels will a bin hold, if it costs $189 more to fill it with wheat, at SI. 05 a bu., than with corn, at 60 ct. a bu.? 63. What is the equated time of the following pur- chases: June 25, $470; July 3, $720; Aug. 1, $860? 64. Find the entire surface of a cone, the slant height being 20 in., and the diameter of the base 10 in. MISCELLANEOUS EXAMPLES. 165 17 14 2 1 7 65. Eeduce i > ? - to least common deriomi- 18 15 3J- 10 nator. 66. A bottle of wine contains 1 pt, 3 gi. ; how many dozen bottles can be filled from a tierce containing 42 gal. of wine? 67. A note is given May 15, 1885, for $500, with interest at 6%, payable annually; no interest having been paid, what is due May 15, 1890? 68. If I sell -| of an article for what -fa of it cost, what ^ do I gain or lose? 69. A square field containing 2^ A. is enclosed by a close fence 6 ft. high; what did the fence cost, at 2 ct. per sq. ft.? 70. In 40 yd., how many meters? 71. What is the fifth term of the increasing geometrical progression, whose first term is 7, and ratio 3? 72. Add all the odd numbers below 25, and find the square root of the sum. 73. What cost 7 T. 14 cwt. 67 Ib. of Muscovado sugar, at 4f ct. per Ib.? 74. An agent kept $560 commission on sales, and sent his principal $15440; what was his rate % commission? 75. Find the weight of 8 doz. boxes of fruit, each weighing 15.4 Kg. 76. What must I mark cloth that cost $8 a }^ard, so that I can deduct 20^ and still gain 20%? 77. What cost a sight draft on New Orleans for $2370, at -^% discount? 78. I bought brandy at $1.25 per gal.; 33|^ leaked out; at what rate per gal. must I sell the remainder to gain 33^%? 79. What cost 10000 feet of canvas cloth, at 18f ct. per yd.? 16C RAY'S NEW TEST EXAMPLES. 80. A contributed $7500; B, $5700; they gain $3872; how should they divide it? 81. A sum of money was borrowed May 22, 1884, at 4^, and $661.38 was paid in full Jan. 5, 1890; how muoh of this was interest? 82. Keduce ^f-y to its lowest terms. 83. What will be the cost of a sight draft on Phila- delphia for $1700, at \% premium? 84. How many times will a wagon wheel, 18 ft. 4 in. in circumference, revolve in going 4 miles? 85. How much will the ground cost on which a man can raisa 728 bu. of potatoes, if each bu. requires 1^ sq. rd., and land costs $7.50 per A,? 86. Invested $7840 in bonds, at 2% discount, and sold at 4% advance; find my gain. 87. How many perches in a wall 55 yd. long, 15 ft. high, and 3 ft, 3 in, thick? 88. What is the largest measure that could be used to measure out 81 gal., 120 gal., and 150 gal.? 89. A horse is fastened by a rope, 60 ft. long, to a stake in the center of a field ; over what space can he graze ? 90. The first term of a decreasing arithmetical pro- gression is 873; the common difference. 2^; find the 200th term. 91. How many cords in a pile of wood 56 ft. 3 in. long, 53 ft. 4 in. wide, and 5 ft. 4 in. high? 92. "Find the hypotenuse of a right-angled triangle, the other sides being 90 and 56. 93. What is the solidity of a globe whose diameter is 12 in.? 94. What will it cost to plaster a wall for blackboard use, it being 11 ft. 3 in. by 5 ft. 4 in., the price being 50 ct. per sq. yd.? MISCELLANEOUS EXAMPLES. 167 95. What is \% of I? 96. If 27 oxen require 33 A. 120 sq. rd. of pasture, how much will 13 oxen require? 97. At If ^ premium, what must be paid for insuring | of the value of a house worth $7200? 98. Bought stock at 12% discount, and sold at 9^ advance ; what % did I gain ? 99. At $1.94 a cu. 1., what must be paid for a granite block 28 in. long, 27 in. wide, and 32 in. high? 100. An agent bought cotton for a manufacturer, charging % commission; the total bill was $17487; what was the agent's commission? 101. Find the value of the stamps required for 75 boxes of cigars, containing 100 each, the taxes being $3 per thousand. 102. Reduce .50625 to a common fraction. 103. What sum at interest 3 yr. 6 mo. 20 da., at will amount to $532.40? 104. What cost 41 gal. 1 gi. of brandy, at $5 per gal.? 105. Invested $7840 in bonds, at 2^g discount, and sold them at 4^J decline; find my Joss. 106. What will it cost to plaster a room 18 ft. long, 15 ft. wide, and 12 ft. high, at 18 ct. per sq. yd., deducting 2 openings, each 4 ft. by 8 ft. ; and 2 others, each 3^ ft. by 8i ft.? 107. What will be the cost of a sight draft on Chicago for $847.30, at \% premium? 108. What would be the largest baskets in which either 350 bu. 1 pk. of peaches, or 250 bu. 2 pk. of plums could be packed without leaving any remainder in either case? 109. Find the convex surface of a cylinder 20 in. in diameter and 40 in. long. 110. In 50 gallons how many liters? 108 RAY'S NEW TEST EXAMPLES. 111. In what time time will any principal double itself at 3^^?_ 112. Find the surface of a sphere, the diameter being 14 in. 113. What cost 125 T. 7 cwt. 9 Ib. of coal, at $4.50 per T.? 114. What is the diameter of a circle containing 3 A.? 115. A man realizes $1800 per annum on $24000; what is his rate of gain ? 116. How many medals, each weighing 3.3 Dg., can be made from 2442 Kg. of silver? 117. What is the difference between the square of 625 and the square root of 625? 118. How many acres in a square iield enclosed with 6 miles of fence? 119. What cost 1000000 in. of twine, at 4 m. per rd.? 120. A note dated Aug. 21, at 90 da., was discounted in bank Oct. 29, at 7^, and $2612.75 given for it; find the face of the note. 121. A co-operative company has 15000 shares, of $50 each; A holds 73 shares; what will be his assessment for a loss of $7920 by fire? 122. Received $51.51 interest on a loan of $367.20, at 5%; how long had it been loaned? 123. Eeduce |ff|| to its lowest terms. 124. If a stream flows 3 mi. 20 rd. in 1 hr. 4 min., ho\^ far will it flow in 3 hr. 44 min.? 125. How many perches in a breakwater 800 yd. long, 11 yd. high, and 5 yd., thick? 126. What must be paid for a fence around a lot 60 rd. square, the fence being made of four horizontal strips, each 9 in. wide, and costing 1^ ct. per sq. ft.? 127. What is the ratio of 7.36 to 7|? 128. 5 + 4 + 7 + a = ? MISCELLANEOUS EXAMPLES. 169 129. Imported 50 casks of brandy, 45 gal. each, in- voiced at 10 fr. per gal. (SI = 5.18 fr.) Find the duty, at $2 per gal. and 50% ad valorem. 130. What must be paid for 5 sills, each 40 ft. long, 8 in. wide, and 9 in. high, at GO ct. a cu. ft.? 131. What will it cost to fresco the ceiling of a room 3G ft. long and 22 ft. 3 in. wide, at 50 ct. per sq. yd.? 132. 6 is what % of 1000? 133. Find the volume of a sphere whose diameter is 44 in. 134. What is the compound interest of $500, for 4 yr., at 8^? 135. What as the least number of books that would make an exact number of either scores or gross? 136. If a man walks 4^ miles in 1 hr., how far can he walk in 5120 sec.? 137. A debt, due in 5 years, was discounted at 7%, $420 being taken off; what was the face of the note? 138. How much grain must I take to mill, to have 154 bushels after the miller has taken out his toll of 4 qt. to the bu.? 139. Find the base of a right-angled triangle, the hy- potenuse being 117, and the perpendicular 45. 140. A bill of exchange on London for 86 8 s., cost $420.12 ; what was the rate of exchange? 141. A man sold 520 sheep, and had 35% of the flock remaining; how many had he at first? 142. If 4 men, in 6 da., dig a cellar 45 ft. long, 1G ft. wide, and 9 ft. deep, how many men will be required to dig a cellar 75 ft. long, 18 ft. wide, and 12 ft. deep, in 3 days ? 143. Keduce 50000 minutes to weeks. 144. A's money is 65% more than B's, and together they have $54325: how much has 'each? 170 RAY'S NEW TEST EXAMPLES. 145. $552.96 was loaned July 21, 1810, at 4|-%, and $666.56 was paid on settlement ; find the date of settle- ment. 146. What is the diameter of a circle containing 785 A. 64 sq. rd.? 147. How deep mast a box be made, to hold 90 bu., if it is 7 ft. long and 6 ft. wide? 148. If 35 castings weigh 48 T. 4 cwt. 25 lb., what is the weight of each? 149. Consequent, 22|; ratio, If; find antecedent. 150. 24% of my land is in corn, leaving 266 A. other- wise planted; how much is cultivated? 151. What cost an abutment 66 ft. long, 22| ft. high, and 4 ft. thick, at $2.25 a perch? 152. Money loaned at 4%, and $709.20 paid, of which $69.20 was interest; how long was it loaned? 153. What cost 475 gal. 3 qt, 1 pt. of molasses, at 18 ct. a qt.? 154. If 800 men, in 30 da., can build a pier 240 ft. long, 8 ft. thick, and 12 ft. high, how long must 240 men be employed to build a pier 360 ft. long, 10 ft. thick, and 8 ft. high? 155. What would be the equated time of paying the following bills: May 5, $230, at 6 mo.; June 1, $250, at 4 mo.; July 5, $320, at 5 mo.; Aug. 1, $420, at 3 mo. 156. Bought lemons 5^ below quotations, sold them at 10% above quotations, and gained $24 on 40 boxes; what was the price per box ? 157. A has 350 eggs; B, 525; C, 280 ; they have boxes made, in which each can exactly pack his eggs; if the boxes are the largest possible, how many eggs will < hold? 158. What cost a farm 180 meters square, at 7000 i per Ha.? MISCELLANEOUS EXAMPLES. 171 159. What cost a sight draft on Charleston for $950, at 1% discount? 160. What cost 4 cwt. 59 Ib. 7 oz. of beef, at 13 ct. a Ib.? 161. Find the solidity of a sphere whose radius is 11 in. 162. The time past noon is y 1 ^- of the time to midnight; what is the time? 163. A man had 450 A. of land, and sold 162 A. ; what % of his farm has he still? 164. What will it cost to pave a circular court 80 ft. in diameter, at 55 ct. a sq. yd.? 165. The last term of a decreasing arithmetical pro- gression of 19 terms is 999; common difference, 7; find the sum of the terms. 166. Keduce \\ bu. to integers. 167. A debt was paid 8 yr. before due, and $420 de- ducted, at 7% discount; how much was the debt? 168. What cost 4355 gal. 1 pt. 2 gi. of ink, at 70 ct. per gal.? 169. A note dated May 19, at 90 da., was discounted June 15, at 4^, and $2.31 deducted; what was the face of the note? 170. I invested $7840 in bonds, at 2% discount, and sold them at 4% premium ; find my gain. 171. At 10 fr. per meter, how many kilometers of cloth can be bought for 100000 fr.? 172. Divide 1 of | by 1 of | . 173. What date 4 mo. 20 da. after Dec. 11, 1885? 174. If a man can walk 3 mi. 240 rd. in 1 hr. 12 min., far can he walk in 2 hr. 48 min.? 175. A note is given June 10, 1870, for $480, with at 5%, payable semi-annually ; interest having > -j and to the least common denominator. 285. Find the volume of a cylindrical log, 15 in. in diameter and 40 ft. long. 286. If each of the four sides of a square field were 20^ longer, how much greater would be the surface of the field? 287. What is the square of that number of which 16 is the cube root? 288. A and B were in partnership; A's capital was $8400, and he received $720 out of $1500 profit; what was B's capital? 289. If a field of 15 A. 100 sq. rd. requires 18 bu. 3 pk. of seed, how much seed would be needed for 18 A. 120 sq. rd.? 290. What sum must I pay for a house, so that after spending $50 for repairs I can gain 5% by selling for $4830? 291. What is the value of the compound ratio : 2 bu. : 3 pk. 15 men : 25 men. 27 da. : 6 da. 180 RAY'S NEW TEST EXAMPLES. 292. What date is 5 mo. 27 da. before May 27, 1885? 293. How large a draft on London can be bought for $5000, exchange at $4.87? 294. A note was dated Feb. IB, 1866, and had accumu- lated $21.84 on settlement, Sept. 19, 1867; what was the amount then due? 295. A could plow a field in 7 da., working 8 hr. per da. ; B, in 14 da., working 6 hr. per da.; how long would it require both, working 9 hr. per da.? 296. $5000 was borrowed July 1, at 5% ; paid July 28, $1000; Sept. 10, $800; Oct. 9, $850. What was due Nov. 6? 297. A tank is 21 in. sq. ; how deep must it be to con- tain 21 gal.? 298. After losing $2600, A and B dissolve partnership, A receiving $25200 ; B, $11200 ; how much had each at first? 299. Bought bonds at 4% premium, and sold at a de- cline of \\%; what % did I lose? 300. A put in $7000 for 6 mo. ; B put in $5000, and received T 5 T of the profit ; how long was B's money in- vested ? 301. A ring, 100 ft, in diameter, was made in a square field 100 ft. long; how much land was left in the four corners ? 302. A man has goods costing him $11200, and gained 5% by selling them through an agent, whose commission was 2% ; what did the agent receive as commission? 303. If 10 horses can haul 50000 Ib. 2 mi. in 4 hr., how many horses will be required to haul 70000 Ib. 5 mi. in 5 hr.? 304. A debt was contracted Jan. 19, 1888, with 9^ interest ; debt, $375. On settlement, $141 interest was paid; find the date of settlement. MISCELLANEOUS EXAMPLES. 181 305. What is the side of a square which is equal to a right-angled triangle whose base is 30 ft. and hypotenuse 78 ft.? 306. Eeduce A\A- to its lowest terms. i o o y & n 307. What is the cube of that number of which 53 is the square root? 308. A malt tub is 18 ft. in diameter and 6 ft. deep ; how many gallons will it contain? 309. A note at 60 days was discounted July 13, at 8%, and $18.36 was deducted for bank discount, and $2411.64 paid the holder; what was the date of the note? 310. A pile of stone is 22 ft. long and 18 ft. wide; how high must it be to contain 96 perches? 311. Take the cubes of all the even numbers under 20; add them, and extract the square root of half the sum. 312. The tax levy being 23.64 m. on the dollar, what tax must a man pay, whose property is assessed at $43246? 313. $512 was loaned at 1\%, and $228.80 interest was due April 7, 1886; when was the money loaned? 314. The fence was removed from a square field con- taining 40 A. ; what would be the area of a field 20 rd. wide, which the same fence would exactly inclose? 315. A debt of $732 is now worth $600, reckoning money at 8% ; how long before it is due? 316. If 15 men earn $427.50 in 19 da., of 10 hr. each, how many days, of 8 hr. each, must 38 men be employed to earn $592.80? S17. The list price is 40 ct, with and 10 off; what is the cost? 318. An agent bought, for a capitalist, ground 400 ft. along a street, charging 2% commission, and drawing on his principal for $18360 in full; what was the price per front foot? 182 RAY'S NEW TEST EXAMPLES. 319. A bin is 6 ft. wide and 4 ft. 8 in. high ; how long must it be to contain 240 bu. ? 320. A note of $000, with interest at 6%, was dated Nov. 13, 1870, and endorsed as follows: July 10, 1871, 100 ; May 7, 1872, $100; April 4, 1873, $100. What was due May 1, 1874? 321. I sold two farms, at $1920 each; on the first I gained 20%, and on the second lost 20^; what % did 1 gain or lose on the two? 322. A man saved $124 the first year, and each suc- ceeding year $11 more than the year before ; how much did he save in 20 yr.? 323. 323f 138f -f 217| 401 = ? 324. What % does a dealer gain who buys 450 bu. apples, at 60 ct. a bu., and sells them at 24 ct. a pk., if \ are lost by spoiling? 325. The list price was 72 ct. per gross, with 20, 25, and 16f off; find the cost per gross. 326. I paid $75.60 for insuring -| of the value of my factory, at -% ; what was the factory worth? 327. A square field contains 160 A.; what would be the area of a circular field with the same length of fences? 328. When it is 6 hr. 3 min. A. M. at a place in 100 E. long., what is the time at a place in 40 W. long.? 329. Find the radius of a sphere whose surface is 380.1336 sq. in. 330. Find the cube root of the sum of the cubes of 27, 36, and 45. 331. At li ct. a sq. ft., what will lumber cost for a platform 200 ft. long, 70 ft. wide at one end, and taper- ing to 40 ft. at the other end? 332. Money loaned Dec, 24, 1882, at 3|%, amounted to $600.99, June 6, 1887; how much of this was interest? MISCELLANEOUS EXAMPLES. 183 333, An arithmetical progression has 10 terms ; the third term is 29, and the seventh 73 ; find the sum of the terms. 331 The sides of a triangle are 25-J-, 26, and 26 in.; what is the surface? 335. A log is 20 in. in diameter; how long must it be to contain 1 C. of wood? 336. A man marks his goods at 20% above cost; in selling at wholesale he takes off 10 and 5% ; what is his gain ^, at wholesale? 337. If a man walks 6 kilometers in an hour, how far is that in 15 sec.? 338. By selling at 64 ct. a yd., twice as much is gained as by selling at 57 ct. ; what % would be gained, at 70 ct. a yd.? 339. How large a draft on Berlin can be bought for $500, when exchange is $.965 for 4 reichsmarks? 340. A note, due June 6, 1879, was discounted at 4%, the discount being $69.60, and the present worth $480 ; when was it discounted? 341. What number, added 3 times to 287 T 5 ^, will make the sum 352-*-? 342. $700 was borrowed May 19, at 7%. There were paid: June 2, $75; June 20, $100; July 15, $90; Aug. 7, $120; what was due Sept. 7? 343. 500 bolts, each containing 8 meters of ribbon, cost 560 fr. ; how much would 375 dm. cost at the same rate? 344. A note of $1600, dated Sept. 17, 1888, at 50 da., was discounted in bank Sept. 25, 1888, and $15 deducted; what rate % was that? 345. Bought bonds at 4% discount, and sold at a profit of 12|% ; at what premium were they sold? 346. What % is gained by selling | of any purchase for what of it cost? 184 RAY'S NEW TEST EXAMPLES. 347. Divide 31 Ib. 1 oz. 10 pwt. by 120. 348. A note is given Dec. 12, 1879, for $1000, with in- terest at 6%, endorsed as follows: June 19, 1881, $41.17; Dec. 6, 1881, $177.83; Aug. 21, 1882, $138.25; May 12, 1883, $30.17. What was due Oct. 15, 1884? 349. Bought goods at 20 and 10 off, and sold them at 10 and 10 off; what ^ did I gain? 350. If a field 50 rd. long and 30 rd. wide produces 27 bu. of w-heat, what will a field 75 rd. long and 60 rd. wide produce in another year when crops are greater in the proportion of 7 : 6 ? 61 3| 7 9 351. Keduce > -> > and to the least common 6-f- 3 T 3 T 8 14 denominator. 352. In 10 T. how many metric tons? 353. Goods were sold at ^ and 10 off; the cost was 30 ct. per gross; what was the list price per gross? 354. What sum, at compound interest for 2 yr. 6 mo., at 10%, will amount to $431.97? 355. A bill of exchange on Bordeaux for 8600 fr. cost $1694.20; what was the rate of exchange? 356. Two men exchanged 60-day notes, and immedi- ately discounted them in bank; the first, at 6%, receiv- ing $2572.70; the second, at 5%; what did he receive? 357. What is the difference between annual and com- pound interest of $10000 for 3 yr., at 10^ ? 358. A pole 40 ft. high stands in the center of a circu- lar pond, whose area is 314.16 sq. yd.; what is the length of a line from the top of the pole to the edge of the pond? 359. The discount, at 6%, on a debt due in 3 yr., is $20.16 ; what would be the discount on it 16 mo. before due, at 9%? 360. The square of a certain number is 2209 ; what is the fourth power of the same number? MISCELLANEOUS EXAMPLES. 185 361. Bought at 40 and 5 off, and sold at 40 off the same list; what % did I gain? 362. Eeduce liii to a decimal. 25i 363. Find the surface of a sphere whose solidity is 11494.0672 cu. in. 364. Three men bought a horse for $150, and sold him for $210, by which A gained $30, and B $18; what had each paid for the horse? 365. What is the difference between simple and annual interest of $100, due in 10 yr., with 10%? 366. Complete the proportion of which the first, third, and fourth terms are 5^, 16-|, and 8f. 367. How many ft., board measure, in a plank 20 ft. long, 3 in. thick, 18 in. w r ide at one end and 16 in. wide at the other end? 368. What is the equated time of paying the following bills: Aug. 5, $290, at 3 mo.; Sept. 7, $410, at 30 da.; Sept. 29, $500 cash; Oct. 4, $600, at 60 da.? 369. A cubical block contains 3 cu. ft. 648 cu. in.; what will it cost to gild 5 sides, at 84 ct. a sq. ft.? 370. A prism stands on a triangular base, whose sides are 9, 12, and 15 ft. long ; how high must it be to con- tain 80 cu. yd.? 371. How many ars in a lot 450 m. long and 49 dm. wide? 372. A man made a 60-day note, which he discounted in bank at 8%, and received $19261.51; it being due, for what sum must he give a 90-day note to redeem it, bank now discounting at 9%? 373. A debt of $660, with 5% interest, amounted to $807.40, May 20, 1873; when was the debt contracted? 374. Goods were listed at 40 ct. per gross, and sold at , 20 and b% off; what did 150 gross cost? 186 KAY'S NEW TEST EXAMPLES. 375. A man took out a life insurance policy for $6000, the rate being $32.65; how much will he pay in premiums in 30 years, if he lives that time? 376. What will be the length of a cubical box contain- ing 512 liters? 377. If 6 men, in 5 mo., have $450 by saving 30% of their wages, how much will 9 men save in 4 mo., if wages have been raised 20%, and they save 40% of their wages ? 378. A railroad, with 280000 $100 shares, wishes to make an extension costing $198000; what will be assessed on a man holding 1197 shares? 379. Find the volume of a cone, the altitude being 40 in., and the diameter of the base 18 in. 380. A debt of $806 was paid July 25, 1886, less $156, deducted for discount, at 5% ; when was the debt due? 381. Ecduce .013824 to a common fraction. 382. A note was given Dec. 10, 1885, for $700, with interest at 8%, payable semi-annually, and interest was paid for 18 months: what was due May 2, 1892? 383. A horse is fastened by a rope, 120 ft. long, to a post in the corner of a square field ; over what space can he graze? 384. At 4^ ct. per ft., how many boards 16 ft. long, 5 in. wide, and 11 in. thick, can be bought for $17.10? 385. The longitude of Cincinnati is 84 20' W. ; at what place on the earth's surface is it 1 hr. 4 min. P. M., when it is half past 6, A. M., at Cincinnati? 386. A note is given May 1, 1880, for $720, with 5% interest, and endorsed as follows: May 1, 1881, $30; Nov. 1, 1881, $20; July 1, 1882, $148. On settlement, $640 was due; what was the date of settlement? 387. Bought bonds at 4% premium, and sold at a loss of 12|% ; at what discount did I sell? MISCELLANEOUS EXAMPLES. 187 388. A dealer imported 24 cases German toys, at 250 marks per case, commission 2% ; find duty at 35%, ex- change being 95 ct. 2 m. for 4 marks. 389. In a four-sided lot the line between two opposite corners measures 66 yd., and the other two corners are distant from that line 50 yd. and 60 yd. ; what is the area of the lot? 390. How much iodine, at 1.3 fr. per Hg., can be bought for 2210 fr.? 391. A ladder 65 ft. long rests against a house, w r ith its foot 16 ft. from the house: if the foot is drawn out 17 ft. further from the house, how far w T ill the top of the ladder slide down the wall? 392. A debt, contracted June 30, 1882, amounted, when paid, to $467.50, of which $55 was interest, at 6% ; when was the debt paid? 393. Goods were bought at |, 20, and 10 off, and sold at i, 15 and 5 off; what % was gained? 394. A put in $9000 for 6 mo.; B, $10000 for 5 mo.; at settlement, A had $9270; how much had B? 395. What is the sixth term of the geometrical pro- gression 9, 12, 16, etc.? 396. What cost 55 metric tons of sal soda, at .15 fr. per kilogram? 397. A man has a note dated Aug. 25, at 90 da., which he wishes to have discounted Oct. 10, and finds that he will receive $9.40 more if discounted at 5% than if dis- counted at 6^ ; w r hat was the face of the note? 398. A merchant, in selling at wholesale, takes off 5% from his retail prices, and gains 14% ; what is his retail profit? 399. What sum at 6%, payable annually, would amount to $935.20 in 5 years, if no interest is paid before that time? 188 RAY'S NEW TEST EXAMPLES. 400. Find the volume of a sphere whose surface is 31416 sq. mi. 401. Two men were employed 3 days to lay a stable floor, 70 ft. long, 30 ft. wide, and 3 in. thick ; wages, $2.25 per day ; lumber, $23 per thousand ft. ; what was the total cost? 402. If a man can fence a lot 100 rd. in diameter in 4 days, how long will he be employed to fence a lot 200 rd. in diameter? 403. If 4i man can plant a lot 100 rd. in diameter in 4 days, how long will he require to plant a lot 200 rd. in diameter? ANSWERS. Article 19. 1. 2019. 2.3625. 3.3289. 4.3479. 5.3213. 6. 4117. 7. 29595. 8. 31980. 9. 33960. 10. 39372. 11. 47467. 12. 408028. 13. 292002. 14. 489641. 15. 500081. 16. 485558. 17. 4009575. 18. 4066552. 19. 4125789. 20. 4246920. 21. 4929077. 22. 4571993. 23. 4627806. 24. 3894072. 25. 59682383. 26. 63954128. 27. 76129904. 28. 59356529. 29. 44609196. 30. 33485205. 31. 22253849. 32. 39479884. 33. 33537. 34. 367958. 35. 318042. 36. 258677. 37. 277670. 38. 304267. 39. 343207. 40. 345280. 41. 237957. 42. 341390. 43. 1045358. 44. 3840490. 45. 2077898. 46, 64138. 47. 44467. 48. 72527. 49. 27803. 50. 27810. 51. 334834. 52. 2126906. 53. $50421. 54. 13602. 55. 1325 pounds. 56. 108410. 57. 1642. 58. 80 feet. 59. 745. 60. 4790 pounds. 61. 2847 bu. 62. $10215. 63. 1492. 64. 60698 ft. 65. 1797. 66. 1314 ct. 67. 399 ct. 68. $34961. 69. 1926. 70. 1185 tons. 71. 584870. 72. 2000 miles. 73. 594. 74. 2690 pounds. 75. $907. 76. 1300 acres. 77. $422. 78. $9404. 79. 540. Article 26. 1. 1734. 2. 46913. 3. 29293. 4. 80808. 5. 2982314. 6. 22222212. 7. 33333323. 8, 34202862. 9. 26411091. 10. 171089. 11, 55000085. 12. 199998989. 13. 367889276. 14. 900090828. 15. 10921812. 16. 87242906. 17. 8999082. 18. 3067534217. 19. 89640055. 20. 800028087. 21. 80727. 22. 2939607. 23. 2286722. 24. 15928384. 25, 228170591. 26. 10052418. 27. 289226824. 28. 1010094950. (189) 190 EAY'S NEW TEST EXAMPLES. 29, 864197532. 30, 376032G. 31. 58990502765. 32, 25G30264. 33. 194398963. 34. 7855426. 35. 191833945. 36. 28775. 37. 4567813. 38. 4994505. 39, 6276511. 40. 87845. 41. 31199027. 42. 1160889. 43. 7914100. 44. 439999099616. 45. 32731990913. 46. $3032. 47. $2469. 48. $747. 49. 273 acres. 50. 67 years. 51. 1789. 52. $1445. 53. $26716. 54. $37028. 55. 2361 feet. 56. 2964. 57. $1557. 58. $8750. 59. 179. 60. 51 years. 61. $9242. 62. 668. 63. 816. 64. 9811. 65. 37196748. 66. 1738. 67. 675. 68. 582. 69. 1625. 70. 1830. 71. 5839. 72. 897. 73. 1405. 74. $523. 75. 447 acres. 76. 1003. 77. 9566. 78. 49018. 79. $1687. 80. 4200 pounds. 81. $20218. 82. $21950. 83. $2414. 84. $3200. 85. $20879. 86. $16590. 6. 12. 16. 20. 24. 28. 31. 35. 40. 45. 50. 55, 60. 64. 68. 72. 75. 79. 83. 87. 91. 95. 33285. 278855. Article 31. 1. 1630. 2. 4404. 3. 3213. 4. 3088. 5. 3582. 2712. 7. 45424. 8. 68376. 9. 38390. 10. 80874. 11. 40922. 55736. 13. 2350257. 14. 4239396. 15. 4617896. 2868922. 17. 2346330. 18. 3661820. 19. 6251157. 5647474. 21. 6391920. 22. 4082406. 23. 2373460. 5570264. 25. 3741367872. 26. 2016536123. 27. 6020532702. 7716935028. 29. 9336976580. 30. 6766294344. 4120819551. 32, 5367983103. 33. 7838070273. 34. 6601. 10846. 36. 9384. 37. 15810. 38. 9650. 39. 12272. 41. 21132. 42. 35446. 43. 262668. 44. 182031. 46. 181482. 47. 528126. 48. 352674. 49. 543567. 224284. 51. 76242. 52. 31602. 53. 291984. 54. 243004. 445842. 56. 766476. 57. 223244. 58. 665042. 59. 374808. 892248. 61. 3093120. 62. 3589662. 63. 3446546. 3856152. 65. 3228646. 66. 5769525. 67. 18076200. 3378012. 69. 1943212675. 70. 3399899130. 71. 3544904533. 41343239335. 73. 7853233038. 74. 27708855662. 9279625278. 76. $6975. 77. $6975. 78. 16464 yd. 1215136 ct. 80. 247101 Ib. 81. 241920 ems. 82. 655960 Ib. $98945. 84. 214727 links. 85. 120955 Ib. 86. 5695 men. $46494. 88. 112683264 gal. 89. 95091975 mi. 90. 92512 Ib. $404499. 92. 45824 trees. 93. 2108295 yd. 94. 133152 Ib. 7218882 vols. 96. 205592 men. ANSWERS. 191 Article 32. 1. 2985192. 2, 8035104. 3, 26710607. 4. 194553198. 5. 64065096. 6, 18757728. 7. 170321895. 8. 604085568. 9. 230351550. 10. 26907755. 11, 19039104. 12. 72785952. 13. 30948864. 14. 52287552. 15. 24088504. 16. 73180665. 17. 33273456. 18. 70882476. 19. 43096405. 20. 52202416. Article 33. 1. 28734000. 2. 4986500. 3. 6200945000. 4. 3845030000. 5, 46835700. 6. 40050008000. 7. 4007089300000. 8. 37088900000. 9. 268938450000. 10. 3477926700. 11. 4859602300000. 12. 76540063000. Article 34. 1. 26550. 2. 3454360. 4. 1578960000. 5. 3745950000. 7. 3581783200000. 8. 256576320000. 10. 23387136000. 11. 56762721600000. 13. 26980167900000. 14. 4141190060. 16. 70740913000. 17. 13815594000000. 19. 131065010400. 20. 128610595000. 3. 438570000. 6. 38467552000. 9. 254356320. 12. 127264680000. 15. 551374704000. 18. 32213776000000. Article 41. 1. 15226312. 2. 8643753. 3. 1428570380. 4. 161401387. 5. 49114887. 6. 246913077. 7. 164608718. 9. 37037037. 10. 7008946. 11. 10580037. 13. 90455625. 14. 97393690. 15. 1410934745. 17. 2000558288. 21. 4365777. 25. 70072815. 8. 12345679. 12. 19146923. 16. 69360054. 20. 94909300. 24. 15432016. 28. 102863457. 32. 920072. 36. 11201960. 18. 505279134. 19. 86420132. 22. 146090535. 23. 98229771. 26. 793651200. 27. 68685608. 29. 333667334. 30. 58007569. 31. 934598. 33. 8896037. 34. 3208901. 35. 7583366. 37. 7855064. 38. 2600209. 39. 5900470. 40. $742. 41. 1274. 42, 415. 43. 1204205. 44. $162. 45. 570 hr. 46. 504. 47. 575. 48. 72. 49. 349 Ib. 50. 429 miles. 51. 128 weeks. 52. 694. 53. $2402. 54. 2499. 55. 273. 56. 1296. 57. $1028480. 58. 15702. 59. 2668. 192 KAY'S NEW TEST EXAMPLES. Article 42. 1. 2738. 2. 4386. 3. 4623. 4. 5387. 5. 9876. 6. 3875. 7. 4639. 8. 9375. 9. 3896. 10. 7199. 11. 50731. 12. 79308. 13. 40065. 14. 40508. 15. 89490. 16. 30972. 17. 92312. 18. 69234. 19. 37401. 20. 38495. 21. 70193. 22. 2038904. 23. 50783. 24. 30700^. 25. 68040. 26. 38905. 27. 133136^3 2 3. 28. 19909. 29. 40893. 30. 60907. 31. 38729. 32. 70625. 33. 4075008. 34. 12144018 Jfff. 35. 67872653f|J. 36. 75690587^1 ft-. 37. 80448947-J-fff. 38. 395. 39. 156. 40. 501. 41. $305. 42. 65. 43. 285 days. 44. 49 miles. 45. 154 years. 46. 78 miles. 47. 3003. 48. 1674 bu. 49. 9208 Ib. 50. 7934. 51. 1925. 52. 107 min. 53. 189 yd. Article 43. 1. 188JJ. 2. 12649. 3. 11641&. 4. 60813fg. 5. 98508&- 6. 20864. 7. 496796J> 7 . 8. 133643^. 9. 1514097- 10. 1894074. 11. 2645501|. 12. 56811JJ. Article 44. 1. 47389^- 2. 3678540^. 3. 2700000 ^ 7 o 4 oV 4. 12345678^. 5. 3704605^%. 6. 98979 T <&%V 7. 1300270^. 8. 123843tfft&. 9. 44872^^%. 10. 500070r<&{ny. H- 3726483952^. 12. 430000. 13. 12345654^. ' 14. 754000^ oA^o^- 15. 4763859jftft&. Article 45. 1, 11823fg. 2. 889842HJ. 3. . 4. 1809855A 8 u 2 o- 5. 560300^-. 6. 1823441^. 7. 365137HM- 8. 101604|fJ. 9. 7153-J^^. 10. 1282840750. 11. Ulktffffo- 12. 4092783tf8g. 13. 14. Article 49. 1. $3296. 2. 146640 ct. 3. $13950. 4. 359 A. 5. 108419. 6. 35 cows. 7. 145 mules. 8. 3088. 9. 336735 ct. 10. $1672. 11. $308. 12. $35. 13. 2184. 14. 51 men. 15. 15 pounds. 16. $7600. 17. $16988. 18. $10360. 19. 69. 20. 169. 21. 3820 ct. 22. 72. 23. $10388. 24. 448. 25. $3736. 26. $6240. 27. $17001. 28. 33462 Ib. 29. 948. 30. $1855. 31. 230. 32. 244477. 33. 97 horses. 34. 385. ANSWERS. 193 35. 82 hogs. 36. 276676. 37. $16. 38. 800 times. 39. $70. 40. 1229 yd. 41. 107677 yd. 42. 2106320 Ib. 43. $1068. 44. 15625yd. 45. $4140.* 46. 268850 Ib. 47. 12250 bu. 48. 362. *49. 262 A. 50. 350 A. 51. $2214. 52. 35100 ct. 53. 216. Article 53.-1. $13.93. 2. $87.493. 3. $29.08. 4. $157.50. 5. $9.099. 6. $12.002. 7. $500.10. 8. $200.003. 9. $99.90. 10. $90.99. Article 55. 1. 9300 ct. 2. $8. 3. 460 m. 4. 18 ct. 7 m. 5. 760 ct. 6. 45000 m. 7. $3.009. 8. 8917 ct. 9. 70000 ct. 10. 10000000 m. 11. 4044 in. 12. 46702 ct. 13. 46700 ct. 14. 83009 m. 15. $123. Article 56. 1. $227.75. 2. $206. 3. $1544. 4. $2028.66. 5. $63.95. 6. $2646.95. 7. $3857.85. Article 57. 1. $33.34. 2. $50.33. 3. $23.91. 4. $224.20. 5. $89.10. 6. $62.37. 7. $309.91. 8. $15138.60. 9. $6317.82. 10. $520.32. 11. $370.40. 12. $170.87. Article 58. 1. $199.032. 2. $354.06. 3. $3675. 4. $520.52. 5. $547.20. 6. $10803.20. 7. $22224. 8. $24.804. 9. $121.176. 10. $261090. 11. $38082.80. 12. $330.75. 13. $10693.20. 14. $3005.60. 15. $393.228. 16. $742.26. 17. $114.72. 18. $115.72. 19. $877.50. 20. $900. 21. $3388.56. 22. $27. 23. $128.25. 24. $99. 25. $1263.50. 26. $640. 27. $13525.92. 28. $783. 29. $563.28. 30. $384. 31. $1275. 32. $398.40. 33. $3738.24. 34. $6494.40. 35. $13125. 36. $7140. Article 59. 1. 150. 2. 525. 3. 625. 4. 740. 5. 438. 6. 735. 7. 4760. 8. 7090. 9. 182 yards. 10. 160 sheep. 11. 6460 needles. 12. 796 acres. 13. 200. 14. 152. 15. 2500. 16. $24.87. 17. $13.572. 18. $40.795. 19. $48.448. ^4 KAY'S NEW TEST EXAMPLES. 20. $15.56. 21. $5.72. 22. $3.056. 23. $7.009. 21 $113.89. 25. $2.80. 26. $48.04. 27. 22 ct, 5 m. 28. 62 ct, 5 m. 29. $.055. 30. $.075. 31. $10104.20. 32. $1.15. 33. 3ct.5m. 34. $9. 35. 48 pounds. Article 60. 1. $4000. 2. $100.95. 3. 18 ct. 4. 45 bu. 5. $24.50. 6. $62.58. 7. $96.32. 8. $81.40. 9. $5.948. 10. $37.98. 11. $1072.95. 12. $71.50. 13. $2673.40. 14. $500.50. 15. $9.25. 16. 400. 17. 216. 18. 80000. 19. 36000. 20. 166. 21. $1071.72. 22. $462.25. 23. 349 days. 24. $203. 25. 2 ct. 26. 79400 Ib. 27. $654.02. 28. $59. 29. 48 gallons. 30. 70 miles. 31. 3758. 32. $2.35. 33. $288.40. 34. $67.54. 35. $16.14. 36. $99.73. Article 63. 1. 309 pt. 2. 581 pt. 3. 1201 pt. 4. 2310 pt. 5. 2864 qt. 6. 74 bu. 3 pk. 2 qt. 1 pt. 7. 180 bu. 6 qt. 8. 6399 pt. 9. 37313 pt. 10. 1929 bu. 11. 78928 pt. 12. 1639424 pt. 13. 400 bu. 1 pk. 14. 1543 pk. 1 qt. 15. 224000000 qt. Article 64. 1. 310 pt. 2. 32 gal. 1 gi. 3. 701072 pt. 4. 2996 gi. 5. 2983 gal. 1 qt. 1 pt. 6. 276544 gi. 7. 3194 gi. 8. 466 qt. 1 pt. 9. 2365 gi. 10. 143 gal. 11. 115500 cubic in. 12. 226 gal. Article 65. 1. 6000 Ib. 2. 11300 Ib. 3. 181501k 4. 15999 Ib. 5. 26013 Ib. 6. 155200 oz. 7. 96325 oz. 8. 6 T. 9 cwt. 45 Ib. 9. 49 T. 4 cwt. 10. 438 T. 5 cwt. 43 Ib. 11. 1239744000 oz. 12. 5 T. 5 Ib. 13. 143771 Ib. 14. 355 T. 17 cwt. 71 Ib. 15. 1250 T. 16. 6 T. 17. 281 T. 5 cwt, 18. 34 T. 11 cwt. 20 Ib. 19. 499 T. 19 cwt. 99 Ib. 15 oz. 20. 9 T. 19 cwt. 92 Ib. Article 66. 1. 1797 in. 2. 1915 in. 3. 13320 rd. 4. 2796 in. 5. 1584960 rd. 6. 157 yd. 2 ft. 2 in. 7. 119 mi. 177 rd. 8. 17939 in. 9. 116$ mi. 85 rd. 10. 1100 yd. 1 in. 11. 12672320 rd. 12. 123 mi. 241 rd. ANSWERS. 195 Article 67. 1. 1220sq.rd. 2. 355200 sq.rd. 3. 1948659 sq.rd. 4. 24598 sq. in. 5. 3993690 sq. rd. 6. 128403 sq. in. 7. 5120000000000 sq. rd. 8. 771604 sq. yd. 8 sq. ft. 64 sq. in. Articles 68 and 69. 1. 30 sq. yd. 2. 66 sq. yd. 3. 142 sq. yd. 2 sq. ft. 4. 40 sq. yd. 5. 80 sq. yd. 6. 27 A. 7. 38 A. 8. 62 A. 80 sq. rd. 9. $85.80. 10. $12. 11. $674.50. 12. $38.40. 13. 120 rd. 14. 20 mi. 15. 780 bu. 16. 9 yd. 17. 9 yd. Article 70. 1. 74 cu. yd. 18 cu. ft. 2. 140268 cu. in. 3. 16 cu. yd. 4. 77 C. 5. 2625943 cu. in. 6. 240 cu. yd. 7. 30 C. 8. 5120 cu. yd. 9. $6600. 10. $375. 11. 10368. 12. $570. Article 71. 1. 268200 sec. 2. 110880 min. 3. 2084583 sec. 4. 5475600 sec. 5. 3715243 sec. 6. 1 wk. 2 da. 7. 31 da. 17 hr. 18 min. 8. 7560000000 sec. 9. 7 wk. 1 da. 10. 525600 min. 11. 132480 min. 12. 2419200 sec. 13. 158112000 sec. 14. 26280 hr. 15. 63244800 times. 16. 200000 min. Article 73. 1. 103104 gr. 2. 103698 gr. 3. 143999 gr. 4. 15 Ib. 1 oz. 19 pwt. 4 gr. 5. 211 Ib. 1 oz. 6. 7506000 pwt. 7. 2 Ib. 7 oz. 5 pwt. 8. 24964 gr. 9. 57840 gr. 10. 21814 gr. 11. 2603 9. 12. 84007 gr. 13. 7 ft 11 g 1 3 17 gr. 14. 36 ft 2 6 5. 15. 42 Ib 10 I 3 3. 16. 896 f. . 17. 24000 nu 18. 72707 f. . 19. 648 lines. 20. 15 hands. 21. 51 mi. 22. 4 yd. 23. 5 ft. 8 in. 24. 80 spans. 25. 117 hands. 26. 40 fathoms. 27. 4 fathoms 1 foot. 28. 100 rd. 29. 135457". 30. 68419". 31. 10 31' 4". 32. 1620000". 33. 360. 34. 2160. 35. 8640. 36. 25 dozens. 37. 50 gross. 38. $72. 39. $70.56. 40. $192. 41. $17.28. 42. $10.40. 43. $30.24. 44. $2.52. 45. $90.72. 46. $17.28. 47. 5760 sheets. 48. 3840 leaves. 49. 34560 pages. 50. 125 reams. Article 74. 1. 1788 in. 2. 40392 gr. 3. 134 sq. yd. 6 sq. ft. 4. 3 28' 20". 5. 10 cu. yd. 21 cu. ft. 1152 cu. in. 6. 17740 gr. 7. 1 wk. 2 da. 23 hr. 59 min. 50 sec. 8. 52 bu. 1 pt. 9. 2016 196 KAY'S NEW TEST EXAMPLES. dozens. 10. 15300 Ib. 11. 103 yd. 2 ft. 2 in. 12. 3317760 cu. in. 13. 709 gal. 3 qt. 14. 5184 barrels. 15. 750 gross. 16. 110592 qt. 17. 165 Ib. 7 oz. 10 pwt. 18. 448224 oz. 19. 23552 f. 3. 20. 33 wk. 12 hr. 21. 949 gal. 3 qt. 1 pt. 22. 4 sq. mi. 162 A. 150 sq. rd. 23. 76800 rd. 21 631 pt. 25. 11491220 sec. 26. 99510 rd. 27. 1 T. 11 cwt. 28. 1 wk. 4 da. 13 hr. 46 min. 40 sec. 29. 81 C. 30. 30816000 gr. 31. 385 bu. 3 pk. 1 qt. 32. 6832800 min. 33. 599616 cu. in. 34. 78039 Ib. 35. 49928 gr. 36. 59940 sq. in. 37. 1234 gal. 2 qt. 38. 277 yd. 2 ft. 4 in. 39. 20 bu. 2 qt. 40. 5740 gr. 41. 512005 sq. rd. 42. 768 cu. yd. 43. 199680 leaves. 44. 13 13'. 45. 125000 gal. 46. 7 g 2 3 1 9. 47. 99 bu. 3 pk. 7 qt. 1 pt. 48. 11520 sheets. 49. 612 sq. yd. 4 sq. ft. 135 sq. in. 50. 31 T. 5 cwt. 51. 2855 in. 52. 4204096 cu. in. 53. 6 sq. mi. 560 A. 54. 8816 pt. 55. 3510055 sec. 56. 4290 rd. 57. 320000 Ib. 58. 961600 oz. 59. 4 cu. yd. 18 cu. ft. 60. 865 gal. 61. 864 scores. 62. 14 T. 5 cwt. 49 Ib. 5 oz. 63. 156 bu. 1 pk. 64. 50423". 65. 1180 gal. 66. 771 sq. yd. 5 sq. ft. 64 sq. in. 67. 187 yd. 68. 11 f. g. 69. 36161 pt. 70. 5 wk. 5 da. 71. 300 reams. 72. 9 T. 73. 62020 sq. rd. 74. 16320 rd. 75. 18 C. 70 cu. ft. 76. $25.20. 77. $24.96. 78. 2 cwt. 50 Ib. 79. 120 gal. 80. $36.27. 81. 120. 82. 368 dozen. 83. $75. 84. $16. 85. $136.80. 86. 1496. 87. 800. 88. 1 min. 45 sec. 89. 768. 90. 1 2(X. 91. $61.25. 92. 5400 Ib. 93. 7 Ib. 6 oz. 94. 2250 C. 95. 56 doz. 96. 60. 97. 640. 98. $3.92. 99. 4096 bu. 100. 200 sq. yd. 101. 5600. 102. $760. 103. 400 doz. 104. 2 da. 32 min. 105. 4 hr. 106. 6 bu. 1 pk. 107. 125 reams. 108. 2000 gal. 109. $9360. 110. $54.72. 111. $354. 112. $18. 113. $.035. 114. $121.50. 115. 6 da. 16 hr. 116. $112.50. 117. 160 T. 118. $144. 119. 3 da. 4 hr. 120. $162. 121. 133 cu. ft. 1176 cu. in. 122. $3.60, 123. $11650.80. 124. $247.50. 125. 2592 score. 126. 3 bu. 3 pk. 6 qt. 127. $224. 128. 376. 129. 282. 130. $460.80. 131. $8640. 132. 75 doz. 133. 331 gal. 134. $66. 135. 16 da. 136. 320 wk. 137. 147 barrels. 138. 1040 bags. 139. 81 da. 140. $171.18. 141. $.075. 142. $76.80. 143. 45 gal. 144. 13824. 145. $2.40. 146. 72 sheets. ANSWERS. 197 Article 75. 1. 60 bu. 2. 900 bu. 3. 192 gal. 2 qt. 4. 31 T. 16 cwt. 11 Ib. 5. 151 gal. 1 pt. 6. 4 T. lOcwt. 7. 177 gal. 3 qt. 8. 79 yd. 9. 57 yd. 1 ft. 3 in. 10. 500 A. 38 sq. rd. 11. 127 sq. yd. 3 sq. ft. 43 sq. in. 12. 34 sq. mi. 330 A. 13. 152 cu. yd. 6 cu. ft. 14. 377 C. 7 cu. ft. 1130 cu. in. 15. 57 da. 9 lir. 26 min. 16. 5 wk. 6 hr. 32 min. 17. 42 Ib. 11 oz. 18. 3 g 5 3. 19. 2 Ib 8 g. 20. 23 score and 3. 21. 119 50'. 22. 61 V 1". 23. 35 Cong. 15 f. g. 24. 1 O. 4 f. g . 25. 361 gal. 3 qt. 26. 253 C. 88 cu. ft. 27. 258 dozen. 28. 4 T. 18 cwt. 29. 102 A. 30. 149 da. 14 hr. 31. 100 mi. 160 rd. 32. 24 da. 23 hr. 36 min. 2 sec. Article 76. 1. 19 bu. 3 pk. 5 qt. 2. 19 bu. 1 pk. 6 qt. 3. 50 gal. 1 pt. 2 gi. 4. 149 gal. 1 qt. 1 pt. 5. 1 T. 15 cwt. 18 Ib. 6. 9 cwt. 89 Ib. 6 oz. 7. 23 mi. 250 rd. 8. 7 yd. 11 in. 9. 62 yd. 2 ft. 10 in. 10. 4 sq. mi. 370 A. 11. 17 sq. yd. 5 sq. ft. 99 sq. in. 12. 199 sq. mi. 639 A. 110 sq. rd. 13. 27 cu. yd. 17 cu. ft. 1628 cu. in. 14. 62 C. 127 cu. ft. 1706 cu. in. 15. 2 hr. 46 min. 2 sec. 16. 4 wk. 1 da. 23 hr. 57 min. 56 sec. 17. 5 Ib. 7 oz. 7 pwt. 18. 2 Ib 9 g 4 Z 2 9. 19. 4 48' 40". 20. 6 reams 16 quires. 21. 1 gross 8 dozen. 22. 6 f. g 2 f. 3. 23. 14 bu. 6 qt. 24. 176 bu. 2 pk. 25. 1 wk. 1 da. 7 hr. 26. 316 gal. 3 qt. 27. 83 A. 40 sq. rd. 28. 3 cwt. 58 Ib. 29. 18 C. 113 cu. ft. 30. 2 T. 18 cwt. 10 Ib. 31. 8 23' 40": 32. 4 g 3 3 10 gr. 33. 276 T. 19 cwt. 70 Ib. 34. 96 hr. 18 min. 35. 21 C. 32 cu. ft. 36. 13 bu. 3 pk. 37. 13 da. 11 hr. 3 min. Article 77. 1. 1 yr. 7 mo. 18 da. 2. 84 yr. 2 mo. 19 da. 3. 67 yr. 9 mo. 22 da. 4. 155 yr. 6 mo. 13 da. 5. 1 yr. 10 mo. 14 da. 6. 6 yr. 8 mo. 24 da. 7. 46 yr. 4 mo. 6 da, 8. 85 yr. 11 mo. 23 da. Article 78. 1. 119 da. 2. 64 da. 3. 146 da. 4. 277 da. 5. 203 da. 6. 195 da. 7. 361 da. 8. 162 da. Article 79. 1. 29 biv. 1 pk. 4 qt. 2. 63 gal. 3 qt. 3. 1 T. 12 c\vt. 75 Ib. 4, 64 yd. 1 ft. 5 in. 5. 23 sq. yd. 6. 2 cu. yil 20 cu. ft. 88 cu. in. 7. 6 Ib. 8 oz. 18 pwt. 8. 2 Ib 5 g. 9. 22? 198 KAY'S NEW TEST EXAMPLES. gal. 1 qt. 10. 78 12' '. 11. 20 reams 10 quires. 12. 276 mi. 230 rd. 13. 55 da. 7 hr. 35 niin. 24 sec. 14. 43 T. 15 cwt, 34 Ib. 15. 138 bu. 4 qt, 16. 1073 yd. 1 ft. 17. 37 bu. 2 pk. 18. 24 da. 10 hr. 20 min. 19. 1 hr. 54 miu. 40 sec. 20. 274 T. 15 cwt, 40 Ib. 21. 489 sq. yd. 120 sq. in. 22. 41 bu. Article 80. 1. 3 bu. 2 pk. 3 qt, 2. 3 cwt. 72 Ib. 9 oz. 3. 3 yd. 2 ft. 4 in. 4. 7 sq. ft. 88 sq. in. 5. 3 hr. 30 min. 40 sec. 6. 3 pwt. 14 gr. 7. 1 3 2 9 10 gr. 8. 7 gal. 2 qt. 1 gi. 9. 7 yd. 8 in. 10. 1 sq. yd. 2 sq. ft. 24 sq. in. 11, 2 da. 7 hr. 20 min. 12. 1 cu. yd. 864 cu. in. 13. 23 bu. 3 pk. 1 qt. 14. 5 gal. 1 qt. 1 pt. 3 gi. 15. 98 Ib. 5 oz. 16. 5 cu. yd. 15 cu. ft. 17. 16 da. 7 hr. 34 min. 18. 32' 26". 19. 249 bu. 1 pk. 4 qt. 20. 7 mi. 206 rd. 21. 3 T. 9 cwt. 40 Ib. 22. 1 bu. 2 pk. 7 qt. Articles 81 and 82. 1. 2 hr. 40 min. 2. 2 hr. 13 min. 20 sec. 3. 2 hr. 25 min. 8 sec. 4. 4 hr. 39 min. 24 sec. 5. 6 hr. 40 min. 40 sec. 6. 3 hr. 16 min. 54 sec. 7. 4 hr. 24 min. 3 sec. 8. 4 hr. 41 min. 9 sec. 9. 6 hr. 36 min. 36 sec. 10. 7 hr. 27 min. 26 sec. 11. 3 hr. 55 min. 53 sec. 12. 6 hr. 31 min. 32 sec. 13. 169 18' 15". 14. 104 49' 15". 15. 152 32' 30". 16. 109 21 X 45". 17. 228 37 X 15". 18. 71 17' 30". 19. 82 21 X 15". 20. 11 56' 45". 21. 1 hr. 56 min. slow. 22. 3 hr. 8 min. fast. 23. Shortened 3 min. 24. 5 hr. 32 min. 25. 10 hr. 36 min. A.M. 26. 2 hr. 32 min. A.M. 27. 6 hr. 20 min. P.M. 28. 10 hr. 16 min. A.M. 29. 6 P.M. previous day. 30. 5 hr. 39 min. Article 87. 1. 3, 17. 2. 2, 2, 13. 3. 2, 31. 4. 3, 3, 7. 5. 2 ? 2, 2, 3, 3. 6. 3, 5, 5. 7. 2, 2, 19. 8. 2, 2, 2, 3. 5. 9. 2, 2, 3, 11. 10. 2, 2, 2, 3, 7. 11. 2, 2, 7, 7. 12. 2, 3, 3, 11. 13. 2, 2, 3, 17. 14. 3, 3, 23. 15. 2, 2, 3, 3, 7. 16. 3, 11, 17. 17. 2, 3, 3, 7, 7. 18. 2, 2, 3, 3, 23. 19. 2, 11, 11, 11. 20. 3, 3, 7, 7, 7. 21. 2, 2, 3, 3, 11, 11. Article 88. 1. 2, 2, 5. 2, 2, 3, 5. 3. 2, 2, 2, 5. 4. 3, 3, 5. 5. 2, 3 ? 7. 6. 2, 2, 3, 3, 3. 7. 2, 3, 3, 3. 8. 2, 11. 9. 3, 7. 10. 5, 7. 11. 3, 11. 12. 2, 2, 3. 13. 13. 14. 2, 2, 3. 15. 2, 2, 2. 16. 3, 5. 17. 2, 2, 2, 3. 18. 13. 19. 2, 7. 20. 11. 21. 7. 22. 2, 3. ANSWERS. 199 Article 89. 1. 12. 2. 10. 3. 9. 4. 7. 5. 4 V 6. 78. 7. 49. 8. 11. 9. 9. 10. 82. 11. 49. 12. 21. ^13. 144. 14. 144. 15. 37. 16. 27. 17. 14. 18. 20. 19. 36. 20. 27. 21. 7. 22. 17. 23. 9. 24. 15. 25. 3. 26. 9. 27. 2. Article 90. 1. 240. 2. 720. 3. 240. 4. 400. 5. 3024. 6. 840. 7. 1980. 8. 4620. 9. 7920. 10. 720. 11. 720. 12. 360. 13. 3024. 14. 14762. 15. 4199. 16. 4225. 17. 5145. 18. 2250. 19. 600. 20. 1848. 21. 25025. 22. 2288. 23. 144. 24. 2880. 25. 702. 26. 2304. 27. 3960. 28. 16200. 29. 30870. 30. 8610. Article 91. 1. 9 times. 2. 3. 3. 24 times. 4. 6 times. 5. 15. 6. 54. 7. 24. 8. 32. 9. 24. 10. 16. 11. 36. 12. 102. 13. 360. 14. 120. 15. 18 (hundred). Article 103. 1. ^-. 2. W- 3. W- 4. Hf-- 5. 6. W- 7> W- 8. if*. 9. MP. 10. *&*. 11. 12. HS^- 13. W- 14- W- 15. W- 16. HF- 17. 18. Article 104. 1. if*. 2. 6. W- 7. ^ 8. W- 12. \ 9 oo 3 . 13. *W*. 14. 17. ii} T 9 ^. 18. ^|F- 19. ?A 3. *$*. 9- W- 10. T 9 ^. 15. * r 3 - 20. 21. - 5. 11. 16. Article 405. 1. 76J, 2. 46. 3. 177. 4. 123^. 5. 362^. 6. 174,V 7. 243^. 8. 145 f \. 9. 16%. 10. 33J}. 11. 403-ft. 12. 152f|. 13. 230. 14. 141 1|. 15. 39. 16. 98^%. 17. 81. 18. 82 T %. 19. 218. 20. 536iJ. 21. 48|f. Article 106.- 1. Jf. e. HI- 7. rifc. s. m. 13. Iff. 14. ffj. 15. 19. T 2 ^:. 20. ff||. 2. 9. 3. iJ. 4. ff. 5. - 10. m- n. * 12. 16. Hif 17. ttfJ- 18. 200 RAY'S NEW TEST EXAMPLES. Article I07.-1. f. 2. . 3. f?, 4. AV 5, 11. 6 . ?J. 7. 1-J. fc. 4}, 9. -J^. 10. f. 11. |i. 12. 5J, 13. -?&. 14. fj. 15. ^. 16. |. 17. A. 18. f. 19. if. 20. f. 21. Article 108.- 1. f8, 4j, t- 2. ig. I*, S8- 3. |J, ||, *, 4. fg, fft, |. 5. M, 4ft, H. IS- 6. f 1, If, 34, j|. 7. }f, flfc, AV, AV 8- A 2 5 , A%, TS, i%. 9. M, /A, M &V 10. J5JJ, A 1 ^, 5 %%V 11. ff, ft, 14, II-, IS- 12. T V a , A 5 5, A% 1%%- 13. 5, A, H, fi * 14. fWc, T St, T*lrr, rfte- 15. Air, A 6 t5, A!y, Hi- 16. T V 2 T, T 6 A, T 4 A, -m- 17. fi, fi IS, { j. 18. ^|, m, m, J&- 19- A 7 A, Mfs, AF, iWs- .20. f, M, fg, |g. 21. JM8, iffl, tffl, if 8- 22. AT, HI. AT. AV 23. ^, &, T 1 ^, yfe- 24. , ft, ff, . 25. W, If. W, !- 26. iff , *, Iff. iff- 27. 18, ftf, 118, IM- 28. m, ff f , T%, A\, A\- 29. iH4, H|, A L A, Hf, -BM- 30. ff, fi, % Q , W, W- Article 110. 1. 2|. 2. 2f. 3. 2^. 4. 2J. 5. 1 5 V- 6. f 7. 24. 8. iff. 9. H- 10. HI- 11. 2/ 5 . 12. 24. 13. itf. 14. 2A- Article Ill.-l. 1^. 2. 2ft. 3. 2f. 4. 2ft. 5. 64|. 6. 1HH- 7. 1.4H. 8. 2HJ. 9. 2f|^. 10. 23|f. 11. 2 12. 98 /,f. 13. 154J. 14. 555|. 15. 1498J|. 16. 2|. 17. 18. 5|J. 19. 14fV. 20. 12|f. 21. 13ft. 22. 2J. 23. 24. 36J. 25. 55. 26. 7&. 27. 2|f. 28. 948-^. 29. 17 30. 85|3. Article 113. 1. 13f. 2. 24^. 3. 8f. 4. 9f. 5. 72J. 6. llj. 7. 8f. 8. 159i. 9. 9H- 10, 19J|. 11. Hf- 12. 199J. 13. 142Jf. 14. 74|. 15. 287.V 16. 26J. 17. 352. 18. 368f^. 19. llff. 20. 327^0- 21. 1864f. 22. 53}j}- 23. 876J. 24. 279JJ. Article II4.-1. A- 2. |f 3. ft. 4. ^. 5. M- 6. US- 7. 8- H- 9- H- 10. T b- 11. 3A- 12. SJJ. 13. 1^%. 14. 7ft. 15. 1 5 4 T . 16. 84J4. 17. 54J3. 18. 652/ r . 19. 578ff 20. 4fiJ. 21. 21fH- 22. 102J. 23. 8989ft- ANSWERS. 201 Article II5.-1. JJ. 2, J. 3. A. 4. A- 5. ^. 6. 2*. 7. 8. f. 9. -J-jJ. 10. 1?. 11. 14ft. 12. 8f 13. 145|. 14. 34f. 15. 154. 16. 84. 17. 320, 18. 675. 19. 3473f 20. 189A. 21. 2441406|, 22. 32}f, 23. 306|. 24. 500. 25. I960. 26. 26f. 27. 9&. 28. 840. 29. 31^. 30. 32130. 31. 5200. 32. 48}. Article 116. 1. 63 T 7 T . 2. 156f. 3. 77|. 4. 21 J. 5. Jf. 6. 18*J. ' 7. 17A- 8. 371 9. 1 T %. 10. 662*. 11. lOOf. 12. 56A- Article 117.- 1. |f 2. if 3.1*. -4.8*. 5. rffr. 6. 1AV 7. A. 8. 10}f. 9. 10A- 10. Trhr- 11. 6f.' 12. 7. 13. 4&. 14. 10J. 15. i^. 16. 2 T %. 17. 7 5 F . 18. 23f 19. A- 20. 5|. 21. /AV 22. 2J. 23. H. 24. 25. f J. 26. 24i|. 27. 5f|, 28. iff. Article 118. 1. 31* ct. 2. 56* ct. 3, 64 T 7 ^ ct. 4. $85. 5. $11*. 6. $6A- 7. $41280. 8. $10|, 9. $4.84|. 10. 45 ct. 11. $1. 12. $177.30. 13. 2. 14. 7*f . 15. 31 |f. 16. 89A mi. 17. $136f. 18. 19 A. 19. 9** C. 20. $16. 21. $125. 22. $12}f. 23. $1.37*. 24. 2|| A. Article 119. 1. 1*. 2. f 3. 1*. 4. 6. 5. 21*. 6. T fo. 7. lA- 8. 5*J. 9. f . 10. 3A- 11. 17*- 12. A- 13. 4|. 14. 4f. 15. 48A- 16. Tfff. 17. 1700. 18. 3ft. 19. 1^. 20. 5f . 21. if. 22. 375. 23. 9*. 24. 95&. 25. J-f . 26. ^fe. 27. 21A- 28. f. 29. 1127*. 30. 2f|?. 31. 1J-* ct. 32. $34**- 33. 57*-J A. 34. A J d - 35. 17-J ct. 36. 17*5 lb. 37. A lb - 38. 45. 39. A oz. 40. $3 A- 41. 9| da. 42. $*|. 43. 12^ yd. 44. 8*f Ib. 45. 7A da. Article 120.- 1. f. 2. A- 3. A- 4. . 5. A- 6. A- 7. ft. 8. |f. 9. A- 10. T*IT- 11. A- 12. *f 13. A- 14. j. 15. A- 16. H- 202 KAY'S NEW TEST EXAMPLES. Article I2l.-l.fj. 2.1?. 3. f|. 4. sVo- 5. H. 8. 7. 31. 8. %. 9. TWV 10. A- 11. if- 12, f . 13. 14. |, 15. f Article 122. 1. 2JJ. 2. 3J. 3. 4f J Ib. 4. $13}. 5. If. 6. $61|. 7. 3^ yd. 8. 33f Ib. 9. 5J times. 10. 8. 11. 13f A. 12. ft. 13. 40. 14. IfJ. 15. Tfo. 16. $16J. 17. 131 yd. Article 123. 1. 132 yd. 2. 4840 sq. yd. 3. 40 yr. 80 da. 4. $3.82J. 5. 22869 sq. ft. 6. $180|. 7. 952 sq. rd. 8. $53.20. 9. $123.75. 10. $33.47|. 11. 112392 hr. 12. $15.31J. 13. $21.25. 14. 35H ct. 15. 29J- ct. 16. $1.89f. 17. 32f ct. 18. 10 mi. 12 rd. 2 ft. 19. 18150 sq. yd. 20. 2 mi. 4 rd. 21. 18817920 sq. in. 22. 12 rd. 23. 9600. 24. 77 yr. 35} da. Articles 124 and 125. 1. f qt. 2. ft pt. 3. f oz. 4. Hi sq. yd. 5. f cu. ft. 6. } da. 7. M <>z. 8. |f pwt. 9. M 9- 10. | sq. rd. 11. rfflft cu. in. 12. || sec. 13. yfr pt. 14. Iff min. 15. fft gi. 16. 2 qt. 3 gi. 17. 12 cwt. 72 Ib. 11 T 7 T oz. 18. 302 rd. 1 yd. 8 in. 19. 153 sq. rd. 10 sq. yd. 108 sq. in. 20. 202 da. 22 hr. 21. 9 oz. 6 pwt. 16 gr. 22. 3 qt. 1 pt. 3^ gi. 23. 7 5 1 9 10 gr. 24. 9 cwt, 37 Ib. 8 oz. 25. 2 yd. 26. V 48". 27. 5 A. 46 sq. rd. 8 sq. yd. 4 sq. ft. 72 sq. in. 28. 3 rd. 1 yd. 3f in. 29. 39 cu. ft. 874f cu. in. 30. 3 f. g 1 f. 3 36 n\,. 31. 10 hr. 57 min. 46f sec. Article 126. 1. ^ da. 2. ^V(T C. 3. TT V? sq. yd. 4, 22Vo cwt. 5. A gal. 6. A bu. 7. yeW <^- 8. 3^ cu. yd. 9. ? V Ib. 10. ^io mi. 11. TirWWo sc l- mi - 12. - 9 J o yr. 13. TrtW T. 14. sH chain. 15. T f ^ gal. 16. ^ bu. Article 127.- 1. ^. 2. gf 3. T V 4. A. 5. J. 6. 7. . 8. A- 9. A T . 10. A- 11. * 12. A- 13, ANSWERS. 203 Article 128. 1. 1 sq. ft. 72 sq. in. 2, 124 cu. ft. 3. 44' 12 /r . 4. 4 oz. 12-pwt. 5. 6 cwt. 70 Ib. 6. 1 Cong. 3 O. 5 f. 3 2 f. 3 40 WL. 7. 191 rd. 2 yd. 1 ft, 4 in. 8. 3 rd. 2 yd. 2 ft. 5 in. 9. 5 d:i. 17 hr. 16 mill. 10. 3 pk. 7 qt. 11. 2 qt. 1 pt. 12. 12 cwt. 9 Ib. 4 oz. 13. 87 rd. 3 yd. 2 ft. 6 in. 14. 2319. 15. 70 cu. ft. Article 129. 1. |g. 2. 145 A. 72 sq. rd. 22 sq. yd. 3. 5J. 4. 13*. 5. AV 6. A. 7. M- 8. 7J. 9. 21. 10. . 11. . 12. T^. 13. A Ib. 14. $5ft. 15. $131.25. 16. $2. 17. T V 18. 26f T. 19. $62|g. 20. 23ft. 21. f 22. $55. 23. A. 24. 2 cwt. 57 Ib. 11 oz. 25. 544|. 26. 270. 27. 264. 28. ff, H> yf > If 29. 18. 30. $678. 31. $11.75. 32. 60. 33. $70. 34. $3368. 35. $4^. 36. $396.80. 37. 1638J \ A. 38. $1415iJ, 39. -&. 40. 6 A. 125 sq. rd. Article 130. 1. $112.50. 2. $49. 3. $77. 4. $420.625. 5. $180. 6. $85.89. 7. $605.25. 8. $1280.50. 9. $31.25. 10. $1351.50. 11. $298.50. 12. $222. 13. $370.50. 14. $631. 15. $14.375. 16. $42.40. 17. $47.43. 18. $1.68f. 19. $1.50. 20. $6.468. 21. $13.50. 22. $13.41. 23. $11.85. 24. $14.90. 25. $30.54. 26. $25.30. 27. 21 bu. 28. 42 yd. 29. $6.25. 30. $1.25. 31. $12.33^. 32. $1.33J. 33. 83 A. 34. $58.66j. 35. $8.05. 36. $137.64. Article 141.- 1. f. 2. M- 3. AV 4. f. 5. V 6. 7. Tfo. B. Hf. 9. . 10. rfJo- 11. A- 12. if. 13. 14. 26&. 15. A- 16. 19g, 17. 3001, 18. 46|. 19. 13ff. 20. 20^. 21. H- 22. 14^^. 23. 9 T fe. 24. H- Article 142. 1. .375. 2. .45. 3. .3125. 4. .44. 5. .26. 6. .1875. 7. .40625. 8. .53125. 9. 1.3125. 10. .01875. 11. .00125. 12. .068. 13. .018. 14. .85625. 15. .0171875. 16. .953125. 17. 1.78. 18. .56179+. 19. .2394+. 20. .4. 21. .75. 22. .9423+. 23. .135. 24. .0418+. 204 KAY'S NEW TP^ST EXAMPLES. Article 143. 1. 153.13. 2. 146.23. 3. 600. 4. .458843. 5, 662.2829. 6. 694.532. 7. 989.1009. 8. 3551.979. 9. 192.06. 10. 2767.9932. 11. 1872.448. 12, 5517.789. 13. 599.4. 14. 1472.827755. Article 144. 1. 27.488. 2. 9.17. 3. 35.8761. 4. 253.125. 5. 256.7989. 6. 225.612. 7. 8.4476. 8. 88.888. 9. 16.92924. 10. 18.825. 11. 49.911. 12. 124.1376. 13. .576. 14. 88.850034. 15. 50895.3573. Article 147. 1. .57227. 2. 222.5. 3, 740.25. 4. .01575. 5. 2377.05. 6. .0006. 7. .093. 8. .00135. 9. .9702. 10. 3696.3. 11. .0021. 12. 2250. 13. .031777. 14. .02121696. 15. 4207.5. 16. 169.119. 17. 294.06. 18. .0797449. 19. 730675.2. 20. 729. 21. 80000. 22. 4503744. 23. 310. 24. 94.87. Article 150. 1. 1.67. 2. 7.53. 3. 2.115. 4. 2.5. 5. .024. 6. 14.95. 7. .00345. 8. 12.5. 9. 400.3. 10. 4000. 11. .21. 12. 41000. 13. .96875. 14. .000025. 15. 4.5. 16. .0625. 17. 9.25. 18. .75. 19. 10000. 20. .32. 21. .06636+. 22. .301003+. 23. .0000066+. 24. 98.21428+. Article 151. 1. .8 pt. 2. .2184 pt. 3. .86 Ib. 4. .99 in. 5. .768 sq. rd. 6. .11664 cu. in. 7. .972 sec. 8. .48 cu. ft, 9. .7452 sq. in. Article 152. 1. 1 pk. 6 qt. 2, 1 qt. 1 pt. 2 gi. 3. 3 cwt, 12 Ib. 8 oz. 4. 50 rd. 5. 250 A. 6. 89 cu. ft. 1036.8 cu. in. 7. 138 da. 19 hr. 4 min. 48 sec. 8, 16 55' 12". Article 153. 1. .0055 bu. 2, .015 gil. 3. .0005 sq. yd. 4. .0000125 cu. yd. 5. .01475 bu. 6. .0003375 da. 7. .000256 cwt. 8. .04875 gal. 9. .0000015 da. 10. .000234375 bu. 11. .0000006250. 12. .00002 yr. 13. .0000125 mi. 14. .00024 T. 15. .000000027+ A. ANSWERS. ' ' ^205 ; . Article 154. 1. 1 hr. 12 min. 2. $16.24. 3. 5 A. 4. $2.185 5. 118 Ib. 2 oz. 6. 42 rd. 7. 36 C. 32 cu. ft. a 128 rd. 2 yd. 1 ft. .6 in. 9. 14 cwt. 95 Ib. 10. 32 gal. 1 qt. 1 pt. 11. $9990. 12. 7 qt. 1 pt. 13. $61.32. 14. 233 mi. 132.8 rd. 15. 38 da. 5 hr. 48 min. 16. .375. 17. 1 pk. 7 qt. .4 pt. 18. 42 sq. rd. 19. 1 cwt. 33 Ib. 12 oz. 20. $109.20. 21. 20 yd. 1 ft. 10.5 in. 22. 158 Ib. 8 oz. 23. $121.80. 24. $65.73. 25. 81 ct, 26. 281 da. 5 hr. 49 min. 12 sec. 27. 9 hr. 13 min. 7.5 sec. 28. $6. 29. 3 mi. 40 rd. 30. $612.50. Article 156. 1. 394500 dm. 2. .09364 Km. 3. 1.23456 Mm. 4. 98765 Dm. 5. .000034 Mm. 6. 74600 cm. 7. .837 Mm. 8. 3700 m. 9. 46000000 dm. 10. 5.8 Hm. 11. 374500000 cm. 12. .6725 Km. 13. 8.9364 Dm. 14. 4.56 Hm n Article 157. 1. 37.468 Ha. 2. 49320 ca 3. 3.8743 a. 4. 3.8743 a. 5. 4387.5 m 2 . 6. .0000457 Ha. 7. .89734 Ha. 8. 583900 m 2 . 9. .3843 Ha. 10. 397000 ca. Article 158. 1. 48 1. 2. 39500 cl. 3. .4937 HI. 4. 583900 cl. 5. 4,57 1. 6. 678.9 cl. 7. 346.92 Dl. 8. 4.2789 1. 9. 3.2584 HI. 10, .047 DL 11. 3800000 dl. 12. 2.97 Dl. 13. .04683 HI. 14. 3870000 dl. 15. 49000 1. 16. .37282 m 3 . 17. .678 m 3 . 18. 303 dl. Article 159. 1. .065 M. T. 2. 4893100 mg. 3. 465.3 Dg. 4. .6543 Q. 5. 87000 Kg. 6. .000937 g. 7. 123456 dg. 8. 8.734 Dg. 9. 88736000 eg. 10. .000000086 Q. 11. .0000765 M.T. 12. .3945 Hg. 13. 3894000 gr. 14. 87300000000 mg. 15. 89.9 Mg. 16. 4890 dg. 17. .4 Mg. 18. 12 Kg. 19. 9.876541 Q. 20. 34560 g. 21. 4800.48 Hg. 22. 90830000 mg. Article 160. 1. 43 yd. 2 ft. 2.8 in. 2. 123 A. 88 sq. rd. 3. 8 cwt. 26 Ib. 11.6 oz. 4. 126 rd. 4 yd. 6 in. + 5. 14 T. 6 cwt. 59.8 Ib. 6. 25 C. 110.8 cu. ft. 7. 2 Ib. 4 oz. 2 pwt. 15.gr. 206 BAY'S NEW TEST EXAMPLES. 8. 654 cu. yd. 9. 747.5 sq. yd. 10. 148 sq. rd. 8 sq. yd. 11. 127 bu. 2 pk. 6 qt. 12. 2.54+ in. 13. 160.9347+ Km. 14. 83.612 + in 2 . 15. 40.4694 + Ha. 16. 76.4526 m 3 . nearly. 17. 12.14 + a. 18. 16.3295 M. T. nearly. 19. 160 HI. 20.249.834 + 1. 21. 500 g. 22. 278.7068 m 2 . nearly. 23. 20 HI. 24. 1 Kg. Article 161.- 1. $41.8874. 2. $295.275. 3. $63.975. 4. $2266.89 f- . 5. 38.4 Ib. 6. $27000. 7. $46.80. 8. $85. 9. $1400. 10. $3800. 11. $10800. 12. $75. 13. $14. 14. 8 hr. 20 min. Article 164. 1. 259. 2. 156. 3. 207. 4. 99.2. 5. 65. 6. 3.3. 7. 7.25. 8. .21. 9. 199. 10. 420. 11. 42. 12. .5188 +. 13. 6400. 14. T jhy. 15. 396 bu. 16. 5 da. 22 hr. 48 min. 17. 48 ct. 18. 355 A. 19. 1 T. 11 cwt, 80 Ib. 20. 3 gal. 3 qt. 1 pt. 21. 3 bu. 2 pk. 22. 58 gal. 23. ^ 24. T V 25. 2?. 26. 144.0285. Article 165. 1. 12. 2. 75. 3. 17. 4. 75. 5. 75. 6. 16. 7. 44. 8. 200. 9. 1000. 10. 75. 11. 125. 12. .2. 13. 22. 14. m. 15. .02. 16. 36J. 17. 40. 18. 150. 19. 150. 20. 60. Article 166. 1. 70. 2. 225. 3. 63000. 4. 175. 5. 320. 6. 5f 7. 390. 8. 75. 9. 2666f. 10. 17.5. 11. 242. 12. If. bu. 2 pk. 4 qt. 13. 3 da. 11 hr. 20 min. 14. 18 gal. 3 qt. 15. 82 T. 16. 23 A. 20 sq. rd. Article 167. 1. 1300. 2. 400. 3. 555. 4. 1295. 5. 150. 6. 37.5. 7. f. 8. 20. 9. 6f. 10. 42000. 11. 55|, 12. 30.4. Article 169. 1. $1900. 2. 95. 3. 16. 4. 128. 5. $1600. 6. 456. 7. 150 ft. 8. 48 A. 9. 600 A. 10. 160 A. 11. 400 A. 12. 1728 mi. 13. 5 ft. 6 in. 14. 42 Ib. Troy. 15. 1 oz. 8 pwt. ANSWERS. 207 16 gr. 16. 2580 gr. 17. 1260 oz. 18. 550 bu. 19. 13J wk. 20. 620. 21. 74$. 22. 46000 doz. 23. 365. 24. 15$. 25. \ $. 26. 126 A. 27. 105.84 A. 28. 294 A. 29. 1395 bu. 30. 175 A. 31. 637 T. 10 cwt. Article 172. 1. $98.50. 2. $2717. 3. 1} $. 4. 2} $. 5. $58.50. 6. $1068. 7. $210.20. 8. $1275. 9. $20. 10. $47045. 11. $45. 12. $218.875. 13. 1J$. 14. $15. 15. $462612.50. Article 173. 1. $1254. 2. $2880. 3. $850. 4. $2750. 5. $2750. 6. $326. 7. Article 174. 1. $42. 2. $3.75. 3. $370. 4. $15. 5. $294. 6. 6| %. 7. 6 fa 8. 20 fa 9. 25 $. 10. 70} $. 11, 77 J $. 12. 220 $. 13. 20 fa 14. 25 $. 15. 33J $. 16. $1.25. 17. 6} %. 18. 20 fa 19. 16} $. 20. 3/ r fa 21. $1340. 22. 10 ct. a yd. 23. $7843.14 nearly. 21 $8163.27. 25. $8160. 26. $7840. 27. 166} fa 28.* $3171.875. 29. 25 fa 30. 66} $. Article 175. 1. 7^ $. 2. $817.50. 3. $60. 4. 28 fa 5. $8791.20. 6. $250. 7. 12%. 8. 40$. 9. $4620. 10. 25$. 11. 5ft %. 12. 5 fa 13. 37i fa 14. 33J $. 15. 25 fa Article 177. 1. J fa 2. ft $. 3. $117. 4. ft $. 5. $12.25. 6. 250. 7. $1378. 8. $66.25. Article 178. 1. $1950. 2. $172.50. 3. 2240. 4. 30$. 5. $261. 6. 7J fa 7. $1680. 8. 350. Article 179. 1. $3555. 2. $35770. 3. $6210. 4. 52. 5. 532. 6. i fa 7. $112.50. 8. 98/ T ct. 9. 41} fa 10. $1431. 11. $1439.94. 12. 216. 13. $1590. 208 RAY'S NEW TEST EXAMPLES. Article 180. 1. $468. 2. 10 ft. 3. 444. 4. 70. 5. $294. 6. $300. 7. $100. 8. $91.80. 9. 80 %. 10. 60 fi. 11. 120 %. . 12. 4[J- fi. 13. 24 %. 14. $3. Article 183. 1. $45. 2. $45. 3. $7.20. 4. $240. 5. $273. 6. 55 ct. 7. $608.40. 8. $80. 9. $9185.72. 10. *526.40. 11. $963.50. 12. $1088.91. 13. $70.56. 14. $39.60. 15. $270.03. 16. $1428.16. 17. $438.25. 18. $816.52. 19. $500. 20. $1073.40. 21. $180. 22. $12. 23. $18000. 24. $18.08. 25. $3.60. 26. $1.10. 27. 80.76. 28. $20.09. 29. $31.76. 30. $13.34. 31. $198.75. 32. $976.50. 33. $487. 34. $600.855. 35. $4179.15. 36. $380.87. 37. $3. 38. $1.65. 39. $1.16. 40. 20 ct. 41. $1.72. 42. $4.41. 43. $4747.90. 44. $6.02. 45. $480.80. 46, $16265.60. 47. $388.275. 48. $475.67. 49. $87. 50. $39.75. 51. $73.20. 52. $119.20. 53. $83.50. 54. $223.425. 55. $150.70. 56. $455.41. 57. $512. 58. $879. 59. $846.25. 60. $1404.16. 61. $556.76. 62. $97.19. 63. $1696.27. 64. $5622.65. 65. $130.76. 66. $76.85. 67. $19.20. 68. $57.76. 69. 1383.47. 70. $278.42. 71. $109.13. 72. $8258.90. 73. $696.72. 74. $549.28. 75. $630.45. 76. $430.42. 77. $507.74. 78. "$787.35. Article 184. 1. $.062. 2. $.097. 3. $.294J. 5. $.250J. 6. $.609. 7. I.480J-. 8. $.239|. 10. $.07. 11. $.061J. 12. $.07. 13. $.016. 15. $.042 V 16. $.020J. 17. $.02^. 18. $.002f 20. $.078J. 25. $88.50. 21. $.080f. 26. $77.04. 30. $16.87. 31. $55.80. 35. $4844.44. 36. $6.38. 40. $1018.36. 41. $105.71. 42. $6712.60. 43. $3. 45. $86.32. 46. $1365. 47. $63.58. 48. $631.94. 50. $110.08. 22. $.38. 23. $.420| 27. $78.12. 28. $245. 32. $14.75. 33. $15.48. 37. $.31. 38. $1460.70. 4. $439f. 9. $.0225. 14. $.023i. 19. $.14. . 24. $13. 29. $191.59. 34. $80.48. 39. $756.16. 44. $439.80. 49. $809.65. Article 185. 1. 3 yr. 2. 2 yr. 6 mo. 3. 2 yr. 2 mo. 4. 25 yr. 5. 12 yr. 6 mo. 6. 2 yr. 6 mo. 7. 20 yr. 8. 5 yr. 8 mo. 9. 2 mo. 20 da. 10. 1 yr. 7 nio. 6 da. 11. 11 yr. 1 mo. ANSWERS. 209 10 da. 12. 3 yr. 1 mo. 15 da. 13. 3 yr. 4 mo. 14. 12 yr. 6 mo. 15. 3 mo. 6 da. 16. 6 yr. 3 mo. 17. 31 yr. 3 mo. 18. 1 y.r. 11 mo. 21 da. 19. 1 yr. 10 mo. 6 da. 20. 3 mo. Article 186. 1. 6 ft. 2. 8 ft. 3. 6 ft. 4. 5 <[ c . 5. 8J READERS. By W. T. HARRIS, LL.D., ANDREW J. RICKOFF, LL.D., and MARK BAILEY. Appletons' First Reader 18 cents Appletons' Second Reader . . . .30 cents Appletons* Third Reader 38 cents Appletons' Introductory Fourth Reader . . 50 cents Appletons' Fourth Reader . . . .50 cents Appletons' Fifth Reader r . . . 90 cents These readers combine the word, phonic, and alphabetic methods. There is throughout a definite method of instruction, easily fol- lowed by any teacher. The course of language lessons accom- panying the selections affords an unlimited amount of additional work. BARNES'S NEW NATIONAL READERS. "Five Books. Barnes's New First Reader . .20 cents Barnes's New Second Reader . .35 cents Barnes's New Third Reader . . 50 cents Barnes's New Fourth Reader . . -7 cents Barnes's New Fifth Reader . .90 cents Prepared on the word-method system, with frequent reviews, script exercises, language lessons, and outline drawings. 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