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MICROCOPY RESOLUTION TEST CHART
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3
PRACTICAL PROBLEMS
akitttmet: j
r«»R THK I'MK «ir
StNIOR C vSSHS IN THH PUBLIC SCHOOLS
AHD MOKK KHPWIAM.V FOK THK rsK o. C.VM.IIUTM
PRKPARINO FO.t KXAMINATI0N8
>r
G. J. McCORMAC
In^ptctor of P^UUic Srhoo/.,, Prince I'.h, ,nl hland.
TORONTO :
W. J. GAfJR .t COMPANY, L.m.trd
1902.
•Jx f : ■ J
M ■ '
Entered according to the Act of Parliament of Canada, in the
oflSce of the Minister of Atrrirulture, by W. .T. Gaok \ Co.
(Limited), in the year one thousand nine IiuiiilriMl ami . wo.
PREFACE.
AuiTUMKTic, it seems, is the subject which receives the
lion's share of attention in tlie majority of our public
schools; yet it is doubtful if the results attained are what
they should W An old criticism on Arithmetic as generally
taught in schools is tliat the work being done is only the
guessing of so many riddles; that the pupil learns the
rules in order to perform "a set of sums," and having
learned "the trick" he hastens "to cipher out" all the
problems under the formula in the same mechanical way.
Certainly, there is in many schools glowing up a schoolisli
dexterity in manipulating figures and finding answers, to
the neglect of a proper undei-standing of the principles, or
even the meaning, of figures. All the work given to the
arithmetic class should be practical. Jt should be for the
most part arithmetic dealing with the real affairs of life,
rt should be presented in as interesting a manner as pos-
sible, and the pupils should be required to direct their
attention more to things and their relations and less to
the figures used iu the soluti.m. Clear, logical and complete
explanations of the method of solution of every problem
worked should be given by the pupils.
IV
ntEFACE.
It was at the urgent request of sorue of the leading
teachers of Prince Edward Island that I compiled this
little work. I have endeavored to give a great variety of
problems, and also to have them as practical as possible.
Those parts of arithmetic which have not been receiving
due attention in our schools I have emphasized.
My thanks are due to Alexander Anderson, Escj., LL.D.,
Chief Superintendent of Education for P. E. Island, for
many valuable suggestions given me while engaged at this
work, also for his kindness in revising the complete manu-
script, and assurances of his approval of the Problems for
use in the public schools of Prince Edward Island.
G. J. McCOllMAC.
Chakloitktown, P.E.I.,
January 2, 1902.
'n^m
i^m^is^'i-'-m-^'m
COKTENTS.
Oraded Problems
Miscellaneous .
puoi'oution .
Interest and J'eiuentaok
Fractions .
Present Worth ani> J)is(
Stocks
Mensuration
Decimals .
Problems Helatino to W
Profit and Loss
Taxes and Dutiks
Square and Cube Ivoots
Measurements .
Exchange .
Stocks
Sharing and Partnershii'
Answers
»unt
>UK
page
I
72
73
74
7«)
77
71)
82
Ki
Si)
8(i
S8
89
!K)
91
92
94
PRACTICAL
PROBLEMS IN ARITHMHTIC
^ 1. A swimmer tukes 22 strokes a i„i„ute, aixl goes
-i yards eacli stroke. IIou- l<.ng does it take liim to
NW'im three-(iuarters of a mile?
2. The total area of three estates is ;j,:,;](J aeres If
the areas v,i the two smaller estates be resiu-etivelv three
hfths and two-thirds that, of the largest, find the "acreage
or each. °
3. When a person is 21 years old, what is his age in
seconds ?
4. Wluit is the simple interest on 22 cc^nts for IT) ye-irs
at 5^ % ? . ' ' '
5. Find the value of
? ot £:> 7s. ] Id. + ^ of £20 r>s. 9^d. - -\.^ of £1 1 12s. Gd
and reduce tlie result to the deciuial of a guinea.
6. How many demijohns, ench containing 2 gals .'] c.ts
1 pt., can he filled from a tank holding 14:3 gals '] ots'
ot w4ne ? to 1 • •
7. If a room is 20 feet long and 16 feet wide, how
many square yar.ls of plastering are there overhe.-nP
II..W nmny yards of carpet 4 yd. wide will cowr the
floor y
8 Pkactk'al Proj5Lemh in Arithmetic.
1. Simplify
2. A inuu failed in })iisiness, owing .1 $1400, ]i $4G00
and C $2000. Tho ca^li imxvcds of lii.s estatt/a.v $500o'
1I..VV inn..h can lie pay ou the dollar, and what anioi.nt
does 7> receive ?
3. Find the area of a rhoinlioid whose length is 10.52
chains, and height 7.03 chains.
4. How many small ciil)es, a side of which is 4 inches,
may be cut out of a large cube wliose side is 8 inches ?
5. Wluit is the cost in Montreal of a sight di-aft on
Hahfax for $2000 at a discount of i| % ?
6. AiTange in order of magnitude :
i)
« ; a ;
2iV-25;4|of 1
1 +
1|.
7. If 10 sheep or If, lambs can eat 40 bus. of turnips
in 7 days, how long will it take G sheep and 18 lambs to
cat 30 bus. i
8. Two settlers in All)erta own adjoining farms of 300
and 5'^0 acres respectively. Th. unite their farms, tak-
ing at tlie same time an additional partner, who pays
them $1000, on the understanding that a third share of
the land m future sliall belong to each. How is the
$1000 to be divided between the original owners?
9. If the planet Mercury moves at the rate of 111000
mUes an hour, how fai- would it move in a year ?
10. Subtract .057 of 2 acres from 7.042 of 1 rood, and
express the answer in square yards and the dccimol'of a
square yard.
on
Practical Problems in Arithmetic. 9
1. IIow many childn'n can bo ncpominodHtcd in a
w'hool room 27 ft. wide, Dd ft lonj:, ft. high, if loO cu.
ft. of air shouhl bo aih.wi-d for each child?
2. Of two watches, ono h)ses 5 seconds and tlie other
ji:alMs4 seconds in 12 honr.s; they are both corr«"ct at
noon on a certain day; when will ono be 5 minntes l)efore
the other, and what time will each then show?
3. Wliat percentage of the h-tters are vowels in the
followingsentence:— "Anthmeti(! is the science of num-
bers and the art of computing them"?
4. Divide .204 by .2; Vm:2--> l)y 24.:}; .*J7r>2.;j by
1(K)()()0.
5. Find tluA Present Worth of $.100 for 19 mcmtlis at
HZ-
G. How often must one go round a square field of 10
acres to run a mile ?
7. Find the proceeds of a note for $186 given for I]
month.s and discounted at the l)ank the day it was made
at 6% per annum.
8. Simplifv ^-^r ^-^^ ^
^ " 9.7-6.4
9. If £1 sterling be worth 4.1 Pauls 9 Baiocchi, and be
worth 2.")^ francs; show that a Napoleon of 20 francs
equals 36 Pauls (10 Baiocchi = 1 Paul).
10. Reduce 11 ro. 11 pr. 11 yds. to inches and find
what fraction of 3 acres the result is.
11. If the price of bread be proportionate to the price
of wheat, and a 10c. loaf weighs 14 oz. when wheat is
worth 80c. a bushel, what is the weight of a 10c. loaf
when wheat is worth $1.12 a bushel?
" 71-^
3.1 X .m
""2.i.i ■
10 PllACTlCAL PllOliLEMH IN AltlTHMETIC.
1. € (1„(.K liulf HM i.Mu.l, in a day us A ui.,1 B cm,
do t.»-..th, r, and />' d.^.s Imlf m nm.-h aj,miu us .1 If ull
t iivo wcrkinj. t.)jr,.th..r can mow 20 ucirs «f l.urlcy in
M. .lays J.uNHong would eucli working by himself take
to mow 5 acres 1
2. Divide 41. 26GG3(58 l>y .or)888.
.'5. Wimt is the siiimre rot.t of l.')241-)7H7.')()19()r)21 f
4. Suppose u town h'vies a poll-tax of $21G 0!) go
that each mau shall i.ny us many e.-nts us the <e are of
men t.> be taxed j what is each man's tax t
f). Write a number that may be classified as prime
<>d< , concrete, integral, simpl.., and denominate. Define'
each of those terms,
G Find tl.e cost of i,ainting the walls of a ro.nn -20
n. hmg 14J ft. wide, and l;) ft. 4 in. high, at V.U.. per
«q. yd., ullowuig for a fireplace 4 ft. by 4 ft. 4 in. and
two windows each G ft. by .'j^ ft.
7. Express /.. of 12s. Gd. + A of 3 guineas + .v of
i4 - -•'„ of 2,\d. as the fraction of £5.
H. If a tract of land GJ juiles h)ng and 4 miles wide
which cost $1.2.1 an acre, be exdianged for the samJ
quantity ui the form of a sipiare, and subseciueutly be
divul.-d into 100 e,iual and s.piare farms, ^ of which
should bnng atsale$11.7r, per acre, f of them $12 an
acre, and the remainder ^jilOl per acre ; what would })o the
profit m the tran.^ .ction, and what the sum of the dis-
tances round all the s(iuares ?
9. Of how many variations will the 26 letters of the
ali)habet admit ?
10. Two ships sail from the same port; one goes due
nortli 40 h-agues, tiie other due east 90 miles. How far
are they then apart?
PnAmrAL PnonLEMs ix Arithmetic. 11
1. A Siimnwrsidc ncrclmnt imirkM an- nrticlo 40%
above ('((st ; ]u> hcIIh it m. ju'count at a discount of 10 %
<.nthe niai'krt pri.-f; Ik, p„vs 20 7 of tlio d. l.„ for coi
lectinj,' it. What ju'r wnt docs lie j^ain or lose i
2. .1 sold H of a piece of land f(.r what '} of it cost
him f Wiiat was the piiu per cent?
3. Simplify 2,.,'„„ + l,,;-.„ + r)„„»,„- + 2.()(M)S7r).
4. Find the area of a s(puu-o whose hide is :J3.25
chains.
r>. A cow is fastened to a stake by a rope 12 feet lon^'.
What si)a<'e can she jrraze over i
G. ExjJH'ss ISs. 4.\i\. as a decimal of £1000.
7. The interest on $S70 for ,.,, certain time at (i7
Ijcr
annum is .$124.41. Find the tinn
8. The discount <.n $,')(;(;.50 for D numths is .$!().,")().
Find the rat( of interest.
9. Wluit is the value of .2.') of ,V of f "*" f of 8 j,niiueas.
10. The width of a room is twice its lieiglit and <me
half its lenfjth, and the contents ar«^ 401)0 cu. ft. Find
the dimensions of the room.
11. IIow many pounds of water Will fill a tank 11 ft.
8 in. by I] ft. G in. by 2 ft. ;{ in., if the weight of a cubic
foot of water be 1000 oz?
12. The price of a certain lot of floods is .$80. If T
buy at 10 % off and sell at 25 % on, what per cent do I
gain f
13. A rectangiilar field, .300 yd. long and loQ yd. wide,
is separated into four cjual parts by two bauds of trees
20 ft. wide parallel to the sides. How large will each
part be, and what will be the ai-ea covered by the trees!
12 riCACTKAr; Pljniil.EM.s JV Al{ITIIMKTI('.
1. A wiinlow ill a JMiniin^^ Imildiiiff is 4."> f.-i-t lii^rf,.
How loun must, u lu.l.hr I,., to n-.K-li tin* window from
flio opposito Hid., of tlio stircf, tliH KtnM't h 'iuir GO ft
wich'f **
2. Expn'ss hy Roman notation (a) lO.lO, (A) 1793.
n. A and /; travelled on the same road in tliM wnme
dinrtion-J at the rafe of ;{•/ mih-s jur lionr, ni-d /; at
the rate <.f r..| mihs jwr hour. If A han Miff mill's the
start, in liow many hours will lu^ Im« overtaken ]»v J!l
4. If I buy a liou.se for .$2!)1(), how larj;e a luite at six
months must I have discounted, at G %, to pay for it?
5. How many acres are then^ in a circle whose eir-
cuniforenco is one mile ?
C. A reetanerular courtyard is 42 ft. 9 in. lonf? and G8 ft.
6 in. wide, a footpath goes -luite through it, and is 5 ft.
C in. in width; the footpath is laid with stone at as. Gd.
per yard, and the rest with pe])l,les at 3s. per yard.
What will the whole cost?
7. The width of a phmk is 2G inches; what must lie
the h'ligth of the i)art cut off, so that it may contain
1 yd. 4 ft. 72 in. superficial measure?
^ 8. What must bo the face value of a 3()-day draft on
Charlottetowi' puriOiased in Toronto at a premium of
li % to cost $3G2r).20, interest G % ?
9. Find the sum of £B*} and (9-fV-25) of 5s. and
miUtii)lv the result bv '" ~ '*"''' •^"iV 3 ,%
' 3A-,^ S + 8-^-.
10. If 11 horses and 13 cowa consume 15 tons of hay
in 45 days, how many tons wiU. 17 hoi-s, ., and 23 cows
consume in GO days, if 2 horses eat^ on aa average, as
much as 3 cows?
i:f¥^:m:.-\;'^x_
PiarTICAI. PifOULKMS I.V AlMTHMETIO. 1 .'5
.nono.'jo
X IKKKKMKMM).
1. Tlio (listji!H'«- round onch of two jrardi'tiH is 2.". rods:
Olio is in tho forniof ju'ircl,., Mio other u s«nmn'. Wliicli
contains tlio nKU-o liind, and liow nincli ?
2. Kxprcss tliefollowinirnnnilM'rs in Aral.io notation:
i'CCCXC, DCCLXXXIX. Expluiu both systmis ot
notation
•l. Simplify:
t (.(MIlH,-))
li
2 + 2
3 + 2
3 + if
4. A morcliant marks lln^ scllinj,' pHc.> of an niliclc
which sells at }{':i.2.->, ALK, one whieli sells at >j«!).()() as
TSII, one which sells at ^7(^ as l^M, and on(3 which sells
at 84c. as I(^ What is his pri\at«^ mark, and what wa,s
tho total cost to liim of (lie four articles if tho first
article is sold at u^'ain of ,'50 7 on cost, the second and
fourth at a gain of 20%, and the third at a jyain of i;5.\ % ?
n. There is a liouso havinj,' thieo rows of wijidows and
three windows in each row; the width of each window is
'{ ft. 1 1 in. Find tho cost of Khizinj; the winch.ws at 24c.
per sq. ft., sui»posinf,' the length of a window in tho firsr
row to he 7 ft. 10 in., in the second row (i ft. 8 in., and
in the third row 5 ft. 4 in.
fi. Find tho contents of a rectangular hoai-d whose
length is 12.J ft. and width 9 in.
7. A owes a sum equal to f of his yearly income. By
saving y^y <»f Iiis income ann ,r five years he can
pay his debt and have $1260 .. What is his yearly
income ?
14 Pn.vcTrr .\L Pkoijlkm.s ix Akitiimetic.
1. .1 iM.iiirlit a Jiorsr. whicli he h«>1<1 io Ji at a 1<W8 of
:: ; /; M.M l.iiM to r at, a loss of 5 / ; C hoM I.im at a
put. of li'j '. How iimch (lid .1 loso if f7 ifuine.1
2. Fiii.l th.. (liff.'rciK'M Ix'twfi'u a «lln'ct discount of 20
IMT (-.•lit aii.l aiscouiits of 1,-) |„.i. cent aiul 5 \n>i' wnt.
n. Writ*' a m'{,'otia1»ln note and drflne it.
4. An ajr."iit ivrnvrd }f!n;]2,,l N) invst in cotton at
24.'. a H)., d.'du.'tinff n^ V commission. How many
pounds did lio Imv?
n. Suppose Mr. A. Canipboll Ixm^dit of Beer & Ooff,
n.iirl.»ttcto«-i., dnrinf,^ the month of March tho following,'
^ ''^- 1<'<> l'''^- of ^*'^<,mr at tli.^ rate of 10 ll>s. for $1.(M),
20 U.S. of cofT.c at tlio rate of 5 ll)s. for $1.00, $2 M-ortli
of tea at 4()c. a 11.. Make out a receipted bill for the
goods, dated Aj.ril 1st, 1!)02.
0. A dealer mixed snpir which cost lie, 9e., and l.V
per pi.und respectively in ecpial (piantities, and s(.ld the
mixture so jis to piin 20 per cent. At what price per
pound does he sell it?
7. The i.roduet of four numbers is 032.25; three of
them are oG.,"), 1.1, and .r.:{. \Vl,at is the fourth ?
8. P^iud the amount of duty a M(mcton tobacconist
must piiy on .30 kej^-s, each weighing 28 lbs., tare 5 %,
which c(.st in Cai'olina IHc. a 11)., if the duty is 45c. per
H. and 12.^ % ad ralorem,
0. The interest on $4.-«l for 3 >ts. 5 mos. 18 dys. is
$7!).04. What is the rate ?
10. A and B can do a piece of work in 40 hours, and
B can do it ak)ue in GO hour.s. In liow immy hours can
A aloue do it ?
msaiw^^^m^i
■m-
¥\ immisams^mmm
Pkacimai, rijoniKMs IN Akitiimktk . 10
1. Fm.l til.- .lifr.rvii.M. iM.tw.rii ll,.> tni(. disi-oiint iiikI
fhHl.ai,k .Iis..«nmfc of sfdiMM) fur ) vr. .'{ „„.s. i:, ,lvs at
' %•
-. Tin- Icn^rfl, of ,1 j,iini;i."loj.ijM»l Is !) ft., l.r... 1, 2 ff.
)f2() aiuldrpthls ill. Find its nolidity. ' "" '
3. Find tl.o l..jr,d tinio of jimtiiiitv of tl.o followii.jr
Mof.., till, u.i.xpind tin.o «i.d til.. i,ro<.n.ds, it iMi,,.. uis-
••omitcd Ai'iil KMli, l!)(t1, at (I ' :
•tn.-».:.() <irorjr,.toun, I'.K.T.. Maivl, ir.tl,, 1001
.NM„.tyd«y.s«ft..r dnl,-, f.,r valu., ,• iv.-d, I ,„o,nis,.
lo I'nv to Howard UsVw, uv ord.r. On., hun.lnd s.-vntv-
liv<' ,;;;, doll.ns. at til.. M.-rcliants' P.,nk of P. H Uhnu]
Soiiris, with int. -r. si.
I'anii.na.s M.'L.'o<l.
4. In an Arithm.-tl.'. an .-xanipl.. was i.rint.-d tlius:
"Ad.I togctlMT V ^ 1 ' •• fl, 1
^ 14j.j^ Ijij^ |.j • >'"' d.iionwnator of
«Mio fra.-ti.a. iM-i,,^' ac.Md.-ntallv 'on-tt.-.i. Tli.. answ.T
unv.., at til.. ...i.I of tl.o IxM.k was m. Ki,.,i „„. ,„.^^^,,.^
denominator.
n. .1, Ti, and rstnrt in lu.sin.'.s.; l.,jr,.tli.T ; .1 p„ts in
.+•..()()(», /.• ^mm, „n.l (' .t!>(.0(). At til.. ,.,Ml .,.' thn...
■"onths C l..,v..s, and at tli.. m.l of H-v.n months //
i«'HV.'s, both takinj,' out th.i.- (capital with th.-m : hut thr
profits a,v m.t divid.-d till tlio nid ..f th.. v.-ar, wh.-n ('
n'<v,v..s $.,(.. Unsv uuivh will .1, /;. ,,„,1 (' ilu-u r.-<...ivi.?
C. K.-du.e ! :» - ''-^ ' X "^ 4- (II f 1 • 1
( 4'ff ' 41 j ^ •■' + •'" i<» Ji decimal.
7. Findlhc value in Cana.lian nion.-v .,f ,, ,.nrst. con-
amin^;U) .ovenM^us, l/i half-sov..n.i^ns, U crowns, ;]G
lialt-.-rowns, a 0111 n.-a, an.I u shilling.
i
I
' •i:^:^iifiii%s?¥fv^?r;ff^
10 rUAC'TICAIi rilOIJLEMS 1\ AuiTllMETK .
1. ^Vli!lt, iminhcr plus 30 % of itself t'cinals 102..") ?
2. A firm sold $4.')(M)() worth of jrojuls in a yciir; | of
tli(» receipts were sales at 20 % profit, .\ at 2.') ^ profit,
and tlio remainder at IV.i^ % profit. What was the total
cost ?
n. How h»n<; will it take $4000 to ^ain $(125 interesi
at ^ % ?
4. Boujrht ^'oods as follows: March 1st, 1001, $200
on2mos.; April (;ili, $S()0on4mos. J Juno 17th, §1000
on ;i mos. What is the average time and date of pay-
ment ?
T). If a child should rocoive 1 cent at birth, 2 cents on
the sci'ond hirthday, 4 cents on the third, etc., how much
would lie be worth when 21 y<'ars of age?
C). If a rhomboid be 80 ft. long and 00 ft. wide, what
is the snai of the area of the two ends which, when cut
off, will leave the remainder in the form of a s(piare?
7. The ])()pulation of Borneo at the beginning of 1901
was 17r),000. If the death-rati' during the year 1901 was
112 ill the thousand and the birth-rate 17% more than
I he death-rate, what was the population at the end of
1901 ?
H. Find tlu; differences l>etwcen a garden containing
s(puire rods and one which is rods >;(piare.
9. ILiw much must I invest in Dojuinion bonds at
142, bi'okerage ^ %, to secure an income <tf §1000, if the
stock pays a dividend of 10%?
10. Being at sea, I saw the flash of a cannon, and
counted 8 seconds between the flash and tJie report.
Kecpiired the distance.
PsACTicAL Pkoblkms ix Akitumetic. 17
Simplify
0""'i:t)-^
f3..^,-1.8;} 1
2_
l.'5t of T).^^
( J).7-G.4 "" 71
3.1x.l()i I
2.i5 j
2. Find tlie value of 500 times the diflference between
an eighty-fourth part of 2.\ ewt. and a thirtieth part of
1 ewt. 3 lbs. (28 lbs. to qr.).
3. A gentleman, wishing to erect a marl)le ehimney-
pieee in his drawing-room, api)li('d to a mason, wlio gave
in the following estimates: —
Length of mantel and slab . . eaeh 4 ft. 8 in.
Sum of their breadths 3 ft. 4 in.
Length of each jamb 4 ft. g in.
Sum of their breadths 1 ft. 10 in.
Find the superfieial c<mtents of the marble re<iuired to
(M.mplete the jol), and determine the value thereof at
??1.2r) i)er s(i. ft.
4. A plot of land is valued at £10:50 ]»(r acre. Wliat
is its value in francs per s<[uare metre if £1 =2r)l- fr. and
a metre = 39|5 in.?
T). Find the s<iuare root of {>i) 41 ()0r)S0()f;2.')00 (h)
r).774409, (r) 1 .-,.'] J, {,!) U3.-3G521.
G. A person, after paying an income tax of 6 mills
in the dollar, has $1090.40 income. What was his gross
income?
7. How many times will a wheel which is 15 ft, 9 iii.
in circumference turn round in going from Charlotte-
town to Cardigan, it being 24 miles ?
18 PPwiCTK'AL PnoiJLEMS IN" AniTHMETIC,
1. Find the valm; of .7 of £1 + .n of 7s. Gd. -2 4,j o
Is. Hd.
2. A toaclior, Lcinj^ aski-d how iniiiiy scholars he had
rei)li('d, ''If I liad as many more as I now liavc, ono-lial
as many more, onc-tliii-d as ni.-iiiy more, and on<'-fonrtl
as many more, T slionld liav«> 2!H;." How niiniy had he!
3. A fjrroccr mixes tea AV(»rtli '}Sc. and 44o. rospoot
ivcly. "Wliat mnst ho tlic sdlinj,' i>ri('o of the mixtni-t
that ho niav f;;.in 1,1 7 (.ii tlio outhiv?
4. ITow many yards of paju'r, 30 in. wide, will Ix
roqnin-d to cover the walls of a room lo ft. lonj,' 1 2 ft
Avide and 8 ft. liiijh? What will it cost to plaster the
walls and eeilinji^ at lOc. per sq. yd. ?
5. A hroken tree rested on the stnmp 20 ft. from the
f?r<mnd, and its toj) tonchcd the jn'onnd oO feet from tho
stnmp. How hi<.rh was the tree?
n. A pirrison of 900 men had provisions for 37 days
at tiie rnto of three rations daily; at tlio end of 12 days
thoy wore roinf(»reod 1)y 240 mon. How long wonld the
remaining i)rovisions last at tho rate of 2\ rations daily?
7. Find the vnlgar fractifm which is e(|nal to the
snin of 15.3125 and 12.007.') divided l)y their diflferiMico.
S. If 25 men, hy working 10 lirs. a day, can dig a
trench 30 ft. long, 12 ft. Avido, and 5 ft. deep in 9 days,
how many honrs a day must 15 men Avork in order lo dig
a trench 48 ft. long, 8 ft. AA-ide. and 3 ft. deep in 12 days?
9. The Anstrian National Del)t amonnts to 2300230850
florins. Express its amount in Avords, reduco its A'alne to
(.nrcuiToncy (1 florin = 1:.. Sd. ; £1 = 4.S(;i-;), and findhoAr
many days it Avonld take to count at the rate of 90 floriu.s
a minute, AA-orking 10 hours a day.
Practical Puodlems iv Akitiimetic.
1!)
(lavi
1. If a i)ik' of wood in tlic fonn <»f a cuW, sold at
i?7.r>() ixT cord, comes to 8;{7o(), what must l.o the Iciij,th
of the pile ?
2. A watch whicli gains 5 sccojrIs in every ,'{ minutes
was set right at (i a.m. What was the true time in the
afternoon of the same day wlien the watch indicated
a <|uarter j)ast -i o'clock?
'.i. Find tlic cost of tiling a roof (,f a l)uilding
vvho.se h^'iigth is;{() ft. and width H yds. j the eaves l.eing
suj.posed to project 1 ft. on each side, and the i-oof n\
such a nature as to form a right-angle at the top ; reckon-
ing at ^4.70 i)er 100 sq. ft.
4. In a ti-aiji containing 240 passengers, the nund)er
of tir,st and third chiss passengers was 202, that of
■second and third chiss 1;J8. How many passengers were
tliere in each class ?
o. A merchant who.se cost-mark is " ('uml)erland,"
lias the cost price marked on an arti- !'^ as BLE. At
what per cent advance must be the scll:;ig price that he
may give a discount of 20 % fi-om the asking price, and
still nuike 20 % on the cost ?
6. Find the value of 5 oaken planks at Gc. inv ft.,
ea(!h being 17A ft. huig, and tlicir widths as f(»llovvs: twd
of loi in., one of 14A in., and tlie remaining two of IS in.
at one end and 11 j in. at the other.
7. Simjdify:
T4 - 7 of •] _ ^ _ i^'f "^ + •• «'f ">
A+ Aof 3i-(Jof ^t-i^ '• dii-if^-
8. Suppose I remit to my agent at Halifax SloOO for
the i)urchase of flour. The flour costs him .^r).00 a bai-rel.
and his commission is 2.\ ^. How many barrels of flour
shall I receive after deducting his coimnissiou?
20 PiucTiCAL Problems in AitiTUiiExic.
1. From a pile of wood 24 ft. long, 4 ft. wide, and
5 ft. high, there were sold 1 J cords at one time and half a
cord at another time. What is the remainder worth at
.*''{.25acord?
2. Find the distanee round a lot of land in the form
of a right-angled triangle, if the longest side is 200 rods
and the shortest 120 rods.
3. A cellar is to be dug whose length, breadth, and
depth are each 12 ft. .'} in. ; find the number of solid feet
in it. ,
4. The capital stoek of a railway is $1437i.Mj, and
its debt is 037,>()O. Its gross earnings for the year 1901
were $2r,()()()(), and its expenses 8132r)00. If the company
paid expenses and interest on its debt at 6 %, and
reserved m^O as surplus, what dividend would a stock-
holder receive who owned 25 shares, par value $100?
5. If the population is now ten millions and the
births are 1 in 20 and the deaths 1 in 30, annuaUy, what
will the population be in 5 years ?
6. Having observed the flash of a cannon, I noticed
by my watch that 6 seconds elaj.sed previous to my
hearing the report. Determine my distanc*^ from the
gun.
7. A detachment, consisting of 5 companies, was
sent into a ganison, in '.*hich the duty required 228 men
per day. The first company consisted of 1(52 men; the
second, 153; the third, 144; the fourth, 117; and the
fifth, 108. How many men must each company furnish
in proportion to the whole number of men?
^^. Find the valup of f "^ f J" J'J, and take the result
'7 X jt X u I
from 10^3^ +71^
.-^fSS \\,, .:-
J -
TT-
■;¥■/■■:■
IF
J
the
PliACTlCAL iMsoiJLKMS J.V AlMTlIMKTK . 21
1. IT(»\v iiumy acres are there on th»^ surface of tlie
eartli, if it contains I'JTOOOOOO s«iiiare mih*s? Express
the answer iu words.
2. A genth'uian in Georjifetown has two huil^linjr
lots, one e«.ntaininj; 40 s(i. rds. and tlie other (10; a
.y< iitlenian iu :\Ioi.taj;ue (dTcrs Idni a sijuare ti.-ld cou-
tainiui^ four times as much hind as liis lots. How many
rods in h'n«;th must each side <»f the sc^uare be ?
3. Multiply 3^ l.y ;5,'„ and divide "l^h.v '^l", and
find the difffjrence Ix-twccn the sum and dilt'crence of
these results.
4. What is tie diflferenci! Ix'twccu .77777 of £1 and
Ss. G.6G48d. ?
5. .1, />', C, and /) enter into i>artnership. .1 and />'
put in ei.'WO ; />' and T, 8131)0; f? and 7>, SISIO; ,1 and
/>, 81010; ^t and C, 61.J00. They gain 81152. What is
the gain of each ?
6. A man huilt a house of three stories. In the
upper story there were 10 wiiulows, each (iontaining 12
l>anes of glass, each pane 14 in. 1)y 12 in. ; the first and
sectmd stories contained 14 windows, each of LI panes,
and each pane IG in. hy 12 in. How many sc^. ft. of
glass were there in the liouse?
7. Find the euhe root of 81 )96;]H4r)12000( )()()( )()().
H. If n is 10 years older than J, and C is as old as
hoth .1 and />', what are their several ages, the sum of
them all being 100 ?
9. On January l;t, ^1 began to trade with 87(50; on
the 1st of February following he took in />* with 8.'340;
on June 1st foUowing he took iu f7 with 8S00; at the end
of ear they foujid they hud gained 8782. WTiat was
ea< tin's share ' the gain ?
22
VllM'TUXL Ph'01JLK.M.S 1\ AlJITHMKTlC
1 Sinij.litA- \'t/" + ^^ ' - ^
11
H.'..)
2. J, HUunVmg „u tlio l«.ft l,»nk .,f riillsl,„nMi.rl
liivtT, (lis<-h;irp..s a f.„n, jin.l /,', „„ tli,' ..ppcsitc l.a.rk
counts liv». pulsatmns <,f ],is wHst Ix'twrn tl..- flash an,
tl.e iv].orf. If s.,un,l fiu-s 1142 tWt p.v s..<.on,l, an.l tla
pulse ot a, iK-rson in lH..-,lfl, lu-ats 7.", sivokvs in a niinuto
mint IS the widtli of the river ?
'i. If tlie unit of measurement l.e 2.{ vds., what is tin
measure of 2i ft. ? - • »
4. Find the value of .02 of £1 +.();} of 7s fid +011
of 2s. 9(1.
r>. If a i)ile (,f wood which is 2.10 ft. long, 40 ft wide
and 40 ft. hiji:h, he thrown into the form of a eul.e and
sold f,.r i of as many d(»]Iars as thv (Mihe would be feet
long, what sum wt)uld the cube briu"- f
n. A i)ieee of work is to be done in 3(5 <lays; 15 men
work at It 1.5 hours a day, but after 24 davs onlv iJ of it
IS done. If three more m.-n are j.ut on, how manv'hours
a day nuist all work to finish it in the given time?
7. The bank discount on a note discounted 2 months
12 days before it was due, at % per year, was .^2;]4.
bind the face of the note.
«. Find the cost of covering the floor of a hall 46i
ft. long ami 14 ft. 9 in. wide, with matting 1^ vds. wide
at 25c. a yard. " '
9. I sold two houses at ^2^44 eacli. On one I gained
8 %, and ou the otlier l(,st 8 %. What did I gain or
lose f
i^'^
PkacTK AI. PnOBLEMS IN' AlflTIIMETH '. 2:5
1. Tlifiv arc thm; towers, A, R, juid C, stniulintr in a
(luv.'t liiu', the iH-ijLrhts of whicli arc m, <H), uml :>{) ft.
respectively. The distance betw.-cii tlie top <,f tower A
and that of B is 1)7 ft., and tlie distance ]«-t\ve..ii the l.ot-
toni of th<' tower B and that of (' is 70 ft. From th<-s,.
(hita tind tlie folh.winjr distances: (//) Vvi,u) the top ,,f A
to the lM.tt(»ni of IJ; (h) from the t..p uf ]i (o il,,. l.„(tom
of A ; (r) from tlie l.oltoni of A to tlie hotlom of P, ; (,/)
fn.m the bottom of B to the toi* (.f ('; (,) fn,ni the'l.ot-
tom of (' to the top of B; and (/) from the top of B to
the t(»p of C.
2. Sold 12S() bus. wheat at $1,'; commissi<.n ;!.]/,
char^res.tr,1.4L>|. Invested proeccds in iron, ..ummi.s.siun'
-.\ %. Find the sum invested in iron.
;]. The solid contents of a culte are 17l*S cu. ft.; {</)
find the leni-tli ..f tlie ,'d,ire; (/>) tin.l the siirfac.. „f ,,11
its faces; (r) lind the h-nj^-th of the diaj^onal am.ss uiw
face.
4. If /', of the i)ri.M' received tor an arliele is h.j^t,
what is the loss jx-r cent ?
5. If a p<.le ]±\ ft. lon.i,' <-ast a shadow I)-,' ft. Icmih-,
how lon.y must a pole lie to cast a shadow 21 ft. lon;,^ at
the same hour of the day?
(). Subtract l.Vl'; from 17,V, ; multiplv t..ireth<T
;;i, In^, 2J?, and ,Vi ; divide a;^^ )»y 2,',;:,, an.l siibtra.-t
the first two results from the last.
^ 7. If the military defensive streugth of the British
Empire is two million m.'ii, what p<'rcenta«,'e of the ar.-a
of P. E. Island would give them standing room, each man
occupying 9 s(i. ft. ?
24 rUA< TI< Ah I'ltOliLKM.S l\ Ai:lTIIMKTlr.
1. A works f«tr (J diivs iit tlu; rntci of 8 lioiirs prr ilaiv
/> works fur 5 hours on tlio first day, niid on t'lich of tli
flvt" substMiuciit days an hour longer than on the prccrdin
day; ^1 docs as niudi in 4 liours as li dors in 5 liouri
If the 8uin total ]»aid .1 and 7> as waj^rs for the wee
be 814, liow much shcudd cacli receive?
2. ITow nniny sqnai-e yards are there in a rliondtoi
whose h-ngth is IJT ft. and hrcadtli ."> ft. '.i in.?
.'}. Th(! lieij^lit of a precipice, standing l)y th<! si(hi <
a river, is KKJ ft., and a hnc^ »»f '.Vli) ft will reach froni th
top of it to the opposite hank. Find the width of th
river.
4. What will ]»e the cost of a lead covering for th
roof of a cathedral, supposing the length of the roof t
he 210 ft. and its width 80 ft.; also the gtitlering 4 f
wide, of the same length as the roof, and to contain
lbs. to the s«i. ft., the r<K>f contaiiiing only at the rate c
8 lbs. to the s<i[. ft., the cost of both roofing and gutterin
being $4.80 per ewt.?
5. The Dr. side of a merchandise ac<!ount is $2r)000
Cr. side is $14784; inventory is $12400. Find tlie pe
cent, gain or loss on sales.
fi. I 1)ought goods in Montreal, costing $802 ; freighi
etc., adds G % to the tirst cost. At what price must th
goods be sold to gain 22 % on the full cost?
7. The distance from the top of a post 6 ft. higl
standing in a yard, to the top of a building on one sid
is 130 ft. ; to the t()p of a building on the other side i
140 ft. ; the first building is 120 ft. high and the secou(
100 ft. What is the width of the yai'd ?
^^'
' ,*'V
PkACTM Ah Pl{()in.K3IS |\ AlMTIfMKTIC. 20
1. Simplify iof ^f of ■;; ^J ..f •;; + i „f ^-^
2. A mill..,- has u J.iu S if. In,,^.. 4J ft. wi.l... 2.^ ft. a.-rp
'•<'M"'j,' 7.. Im.s. How (l.M.p must 1... ,„,,kr Mn.'tl..-,- hi,,'
wl„,.l, IS 18 ft. lo„g a,.(l ;{;; ft. wid... to hol.l 4:,() bus. ?
3. If H pi..,.,3 of laji.l, m n„ls i„ l,.„^rtl,, 1„. 20 rods
wide at o,„. e„d H„d at th„ oti,.-,- tr,-,„i„at('s i,i an u„gl,.,
wliat nii„il)«.r of s(p,a,-(' rods docs it (;o„tai'i ?
4. A dealer \un\>rht a (|uaiitity of I,,,,,!.,.,, for S7(K)
At what pWco must ],e st-ll it s<. that he n.av <liseo„„t
-0/ o,i nski„j? i)riee, allow 10 ;' of sales to hv, l.a.l, imy
-'A % eo„„„issio,i for sellinjr, a'ld still n.ake a in-ofit of
40% <m cost?
'■). Find the eoatents of a wall whieh is 02 ft fi- i„
lonj,' mid U ft. H i„. hiirh, the thi('kiie.ss l)ei„g 2A l.rieks.
T). A fanner borrowed fi-om liis iiei.rhl)or part of a
hay-riek, the pai-t i,ieas,„-i„jr (j ft. ju l,.„irth, lnvadth and
thiekjies.s. At the next hay-season, lie paid liaek tw.»
c<inal euhieal j.ieees, each side of whieh was 4 ft. Has
the debt been diseharged ?
7. If r, eo,nposito,-s in Hi days of lO.i h,-s. eaeh ean set
in typ.» 7L'0 pages, each of (i() lines, with 40 Icttei-s in a
line; in how many days of 7 h,-s. each will coniposito,-s
sot 0(50 pages, each of 4r, li„(.s, with oO h-tic-s in a lim; ?
S. A l)ottle filled with pure wiiKi contains IG d,-inks or
parts of a certain ineasu,-e. If I take -,\ out of this
and fill the b«.ttle with wate,-. then take another ,'„ out of
the mixture of wine and water, and fill the bottle again
wuh water, and so on until I liave taken IG drinks' out
of it, how much wine does the hist or IGth drink
contain ?
2(i Tkai IKAh Pitor.LKMS I.N AlJlTIIM KTKJ.
1. Siinplit'v :
(O I I
of
1
u
«.r
•i + i
V - 1 .J
2. Tlic It'ii'jtli ut' H rod. I is treble its width; the eos
of fj(»oi-iii<r, jil, 7s. (id. I er sij. yd., is tl2S 2s. (Id., und tlia
(»f i»:iiiitiii^ tlie f'tiir Widls, ut 4.]d. pei- s(|. ft., is uls
t;2S 2.S. (id. Wlitit is tht^ liei«,'ht of tlie room ?
;{. If ilie first term of iiii urithtnetieid i>r<»^ression be T
the «'oiiiiintii ditT'er«'iiee 2, iiiul the uuiuImt of tenuis ]'.
whiit is tlie last term ?
4. There is ii ti'iaiii;idar eoi-iifteld who.se three sides jir
l.'jO, 20(>, and 2.')() yds. respecrtively. Find th<^ (ro.st o
reai>ing the eoi-u at $2.42 {u'r acre.
."). A j;roeer Itoujilit snj^ar amonntin^' to $725 o
1)0 days' time, but heinj^ (ttTei-ed 4 ^ off for easi
borrowed the money at a 1)aiik for the time, less f;rae«
at 9 7, and eashed the bill. What was the face of th
note if
(>. 2.") ]H'r eenl. of 2 is what jht eent. of .'{o.^ per <',enl
of (i?
7. A ladder, 4<» fl. lon^^ may be .so placed that it sha
reach a window 'A'l ft. fi-om the j^n-ound on one side o
the street ; and by only tni'ninj; it over witliont movin
the foot out of its place, it will do the same by a window
21 ft. hi.uh on the other sidt'. What is the width of th
street ?
8. Tlie cost of carpeting a room IH ft. lonj? by 16 f
wide, with carpet worth .$1.20 a yard, is $,")!. 20. Ho'
wide is the carpet f
*• V .^ %
P|{.\rTUAI. PlMMII.KM^ l\ AlJll HMKTK . 27
>
ides Jin* I
<M)Stf of
I. How I
1. Houjrht !)»»(> iKTfs of land for H'l-'MMt; old onf liftli
of it at .frj mi ni'i-f. oiif-tiiird of it at !f<l."» an a<Tf, and
tlu' r«'inaind«'r f(u- .+20 an a.-n-. Did I piin or lose, ami
how nnicli f
2. What must 1m' flic ratf of watrcs, thai IJ nit-n may
oarii in 10 days iho same aiMouiit that !l nun •miii in It
days, at $!..■)() |M'r day ?
3. iMaki' an ori^^inal i»rol>l»'ni for ••arpctin^r the Moor of
;i rootn, or for i>last«'i-in<,' or pa|Mrin«,' the walls and
ceilinj; of a room, and ^'ivr the soli-ti mi in fnll.
4. The diaj;<»nal of a st|uar<' (h-ld is l_'(i rods. Kind
tnt' area in at'i-t-s.
5. licdnce .48 of a sq. rod to tin- dtM-imal of an ari-f.
G. If 1.') quarts (»f milk will niakf 2 llis. of hnltrr.
and () lbs. of butter nM|Mirt' as innrh milk as ;i(» ll»s. of
chccst', and 40 lbs. of chtcsf be ma<lt' froir 2 cows in ;!
(hiys, how many quarts of milk, at that rale, would !'.'»
cows jrivf in (> months? If the milk sell at .")••. a (jnart.
the butter at 2'u: a lb., and cheese at lOc. a lb., which
would b<; the more ju-oMtaldc, for the "■ivcn tinic — tli,.
selling of milk, the inakin<r of bnttci-. or the makin" of
elu'pse ?
7. ^l and />' to^'ther can d(» a jfiecc of work in 12
thiys. If ,1 can ch. only ;^ as much as />', how loin;- will
it tak(^ each of them to do the work?
H. Find the area of a trian<r]e whose base is IS.l yds.
in h'ng:th an<i its i>er[>eiidicular altitude l,"i{ yds.
111 ' •< •> ^ - I J I
l<>i?-(4fU:5H) -1
x(4i <»f (;^+ .^)-!4>i of ((i^+ ••,! I
•>• Simplify: I ,-j\ ";' ^u: + 2r.
28 PiarTK Al. ritOlJLKM.S IN Al{ITIIMKTi( .
1. TIk' iMtpulution of a certain town, a<M'<»r(lin(x to
•••'UHUs of IM'M, WHS fi.'no, an iiici-caMr of IS / nwr '
«'«'nsn!s of IHSI, and th<5 census of ISSI showed a jjaiu
2.") % over tlie iiopiilation nf 1H71. Wliat was i
popidation aeeordinj,' to the eensus of 1H71 y
2. There are r»7 Itoxes of rice, eaeli eontaininp oij
hundred and nine thousand tiiree hundred and n
KHiins, and 70 other l)oxes, eaeh eontainin;; seven hi
dred and nineteen thousand two linn<h-ed and nine
tour ^n-ains. Write in words how many ^n-ains «>f r
there are altojjether.
.'{. Sailing' into ('harh»ttetown harltor, I saw the ftti
of a cannon, and counted H seconds l>y niywat<-h ltetw(
the flasli and report. Find my distance from Pi
Kdward.
4. A calde which is 3 ft. h)ng and 9 in. in circu
fennce weijrhs 22 Ihs. Deterrvji; ;'i(« weij^ht of a eal
who.se diameter is 9 in. and lenjrth 1 fathom.
T). Feb'y 2Hth, 1901, I IxMifrht a l)ill „f jro,»ds amoni
inj; to !{i(58r>.4(> on tlie following; terms: ".'> months n
or h-ss 5 % if paid in 1,") days." How much will
recpiired to .settle the hill March 14th?
6. Wliat must he th(> face of a note, .so that win
di.scounted at hank at 7 % for 9 months the pr<»cee
will be $:){){)?
7. The ])ase and hypotlienu.se of a right-an^ded t;
an^de are respectively 7.6 in. and 9..") in. Find the pt
peiidienlar.
5. A traveller, on reaehiufi: a <'crtain place, found th
his w.iteh, whieh kept eurrect time for tli.- j.laee lie lei
was 2 lirs. 2.j miu. slower tlian the local lijue. Had J
travelled eastward or wcstwai-d. and how far?
U'.
VuA^ru .\L PifojJi.KMs j\ Ann
niMKTlr
2'.)
m fo tin*
• >v«'r tlu'
II ^uiu of
wtw tbp
inp cijfht
iiiul iiiin'
Veil Imn-
il iiiiu'ty-
is of ri('«*
the flash
l>('t\V«'(Ml
Dm Port
I circmn-
r' a ('«l>le
ainoiint-
lltllS lU't.
will be
lilt when
ixhil tri-
thf per-
1111(1 thut
' lie left,
Hiul he
1. A iiitrejiunt iiicroHHed l,is capital the first v,.ai- by
•••"-M»»'-t"»- «'f" itself, the H.'eoM(l year hv two-fifilis. the
fliird year he lost tvvi.-sev.„tl,.s of ,,11 h,. |,n,|. uimI* had
*1.>(KM) remaiiiiii^r. \vi,„t was his capital at first ?
2. The (li.imeters of twoeoiireiitrieeirel.s are 1.-, and
U» ft. Find the area of the rinj; formed hy these eireh-s.
.'{. Find the e<»st of pnintinjr the fo„r sich-s and the
iK.ttom of n tank 2\ yds h.njr. 4 ft. wide, an.l 4.4 ft.
deep, at Sc. per .sq. ft.
4. If the iiumlu-r of s.piare miles in the Hritish Km-
\ pire he 1;{0(iO(HM» and the i,opnlation 4:.(KMMM»(K), how
many per.s.ais are there to the sipuire mile ?
5. If :> horses eat as mneh as eattle, and H horses
and 12 eattle eat 12 tons .,f hay in 40 dnvs. how mn.-h
hay will he n-ipjired to k.rp 7 h(»rses and" l.". eattle (I.",
days?
(». Redne,. .1 ,-);}( W};.") tons to ewt.. Ihs.. oz.
I 7. A merehant Imnjrht tea at IS,., a Ih., ami mark.-<l it
tor .sale at 2.1,..; l,„t, aftrrwanls marke.l it np L' ' on
.•iskmjr pnee. at which pri,-e h,. sold I(K> ,.h,'sts awrajrin^'
<0 ll)s. eaeh. Th,' pnivhaser havinj; fail .l hefo.-e pa\^-
ment was made, a .'onipn.mi.se was etre,-t,-,l at 7S,.. on the
dollar Did the .s,.]],-,. jrain or los,', ami how nnwh ?
S. The lenjrth of rt i.ie,.e of timl)er is 2(M ft., the wi.lfh
at the jrn.ater end 1 ft. 9 in. and th,. thi,.ki.,..ss 1 ft ;{ in •
at the l,..ss,.r end th,' wi,lth is 1 ft. in. and th,. thi,.km.,ss
1 ft. What is th,' .soli,lifyy
I !). Ascpiare mil,' has h,','h ad,h-d to the Hritish Em-
pire evry 8 minntes of (^n.'.-n Vietoria's r,'ijrn. If h.r
r<-ij:n dates from o a.m., .Iini.- L'Oth. ls;!7 f,, ,-, ., ni
.Tannary 22nd, 1!)01, find tlie amonnt of l.-rrifav aihh-d
to the Em])ire dnrinj,' her reiL'ii.
..(, 1>UA(TMAL PhoULKMS IN AUITIIMETK .
1 Tn .. citv of :.7S40 iuhaUilauts, .12.> of tin- mf'^^
^ 1....^ ..ft<.n«l tilt' DuVtllc scliool^.
how iiiiiny sHioliirs aTun<i m' l'
,,„ ,„„i „,.,.,.,„„a „„ ..rt.T "";''•■;>„''• ';.,t-ai,i u i.id for
a. Firnlll. mi,..,n,a i,,.. .vs, .m *l.i,(l t... -. xi- ■"
.•„,;.,," 7.-, .n.l Vl-1 li.,Ks. ana ..,<■ l...-,,...,..-,,!,,, .1..-
8. W„a, V--;" ■;;';'\ ' . H, Uvay is ,1... .listau.-..
and Suniincrsule h\ i • '- '; .
iM.tw.M'U Mount, Strwivrt aiul .>ouns .-^
. 11 .;- for 4?f)()(U» For wliat must
., Hou-l.t a l.ousi- and lov toi i^i.nui.. ^
T t it to ..-.un C. ' <"' n-.vino.u'V, and to i.a> ^-'-\;' '
T rent it to ^aiu . ^^ y , .» <,t
,„j„i,s,$22.r.OforiHsurau.-.',auatav..it l.» ,
''';:r:.a..,.a,.«an.,.n...nsi,,-.uH._^^;^
^vi"''-'''V'^:r; r- unL^^ ^'■^
su.d.astow..i^hSlbs.totl,.-s.,t^.
Practical PuonLEMs is Auitiimetic. 81
1. What nnmiv, ',.; ti.at wliich bcinj; iiicrcjisoa by f of
itself and thev ilonblod, j^i-es 4 more tliau the square
root of 2704?
2. Simplify: u.:, X ;.t-42S/i x 1.07n92;{o X .;{
.6 X 2.!s.-)714i! X 2.;!(»7()!):> x 14..')
.'{. What mm bears the same proportion to £.1 that VAs
ll.i<l does to £3 14s. 4d. y
4. A eertain partition is 141 ft. r> in. lonir and 11 ft.
.'5 in. hifrli. How m.-my .sq. yds. does it eontain ?
5. A woodman hewinjj: timber strnek so vijron.nsly
that I heard .-Meh stroke of his axe, aM<l counted .", l^-at's
of my pulse between each stroke. How far was the
woodman di.stant fro7n me, r.'ekoninjr pulsations to
<•lap.se durinj; the time that sound takes in movin.. a
tnile ? *"
(). What is the difference between a field (10 rods
scjuare and one containing (JO s(]. rods?
7. A aj?j-eed to lal>or for .t2..-,0 ])er day on condition
that h(> should forfeit 50... for everv (h.v h.' was idle At
the end of 100 days he received .$190. How many days
was he idle ? ^ . ■
8. WHiat is the length of a rope extejiding from tho
top of a pole 40 ft. high to the top of a stak.' 1.^5 ft. hj.^h
standing 3.3 ft. from the pole? ^ '
9. A cistern that holds 280 gallons i.s empty It has a
•^"I'ply pipe that will fill it in 10 hrs. an.l a discharge
pipe that will empty it in 7 hrs. If, after the supply pipe
has been open 4 hrs., the discharge pipe i.s opened, in
what time will the cistern be emptied ?
s
1
T^mMWr>-
.'r^mm^^._:yt.
*;Lv»:ni^:^-:^i^^^«uA
32 PuACTKAL Problems in Auitiimetic
1. Multiply If) l)y sixteen Imndrcdtlis, divide the pro-
duet by sixt.Vu tcn-tliousaudtlis and express tlie qiiotieiit
in Roman notation.
2. Find the square root of tlie third power of l.G
correct to 4 decimal places.
3. A S(iuare lot is l.ordered hy a walk 1 yd. wide; the
lot and walk to^'ether occupy 2.\ acres. Find the cost of
paving the walk at 25c. a s(i. yd.
4. Write in fitrnres: Eight hundred trillion, eight
billion, eight million, eight hundred thousand and eighty.
5. A receives a, semi-annual income of $180 from
(\P.R. stcx'k at C %. What was his total investment if
C.P.R. stock is (luoted at 1 lO.J, bn.kerage i of 1 per cent. ?
G. King Edward VTI. was boi-n on November 0th,
'841. Find hi> age in minutes on November 9th, 1901.
7. Divide G dys. 5 hrs. 10 min. 30 sec. by V>, and
multiply the result by 1 U.
H Sold goods at a gain of 20 %. If Ilu> eost had been
$(i() less, the gain w<.ul.l have been 25 %. Find the cost
of the goods.
9. A brewerj' is worth 4 % less than a tannery, and
the tannei-y IG % more than a boat; the o\Anier of tin
}>oat has traded it for 75 % of the brewerj^ losing $103
What is the tannery worth ?
10. If the interest on $1 at (> % is $.0835, what is tlu
time ?
11. Fiml the cost of 735 fence boards, each IG ft. lon«
and 5 in. wide, at $14.50 per M.
mik.m.. \^m
WP^«
PlfACTlCAL PhoHLKMS IV AlMTHM KTIC.
i
1. It ni I'.Wli.yslfiOmni, working 9 hours a day, exca-
vate a e..t 900 ft. long, ]:{ ff. d.-ep and .'50 ft. wide ,n
limv many days .sluM.ld Or, men, M'orking H hours a dav
.'x<-avate anotln-r .-.it 1l>()() ft. ]„ng, G.^ ft. deep, 38 ft wide'
and 2i times as diflrteult to excavate ?
2 If in building the Belfast Kailway, rails weighin.^
SO ll>s. to the yard be used, how n.anv t<.ns of rails ^^'ill
be re(iuired to finish one mile of the road ?
^. Divid.^ three ten - miDiouths bv five hundred-
thousandths.
4 Find the cost .,f 24 planks 10 ft. long, U in. wide
.-.ud 2i m. thick, at $L>;5..-.() p,.r M, board m.-asure.
T). A stock of goods valued at eiH.lOO is insured for ''
<'f Its value at 1 J %. Find the premium.
r.. How many shares Bank of Halifax stock can b,'
p.n-chas,.d for .t22:}7.7r, at 12!)=^, l,rok,'rage i per cent ?
7. Expre '" words 301 4,")Ofi.87.")4.
5 The r. • a roof is W ft. G in. above the eaves
and the eav. .s are 55 ft. apart. Find the width of on.'
sule of the roof.
J). If milk weighs m lbs. to a cu. ft., and water (L\i
li)s., what per cent is milk heavier than water ?
10. If the interest on $100 for 3 yrs. 4 mos. at G ^' per
annum is $20, for how long must $350 remain at int^^-est,
at U / per annum, to produce $42?
irulVn"'*'??""'' "'■'• ''^ ^''''' ''''" ^'"^ ^•'^*"l"'''-eJ to make
1000 lbs. of bread, if the bread weigh 30 percent more
than the flour used?
1 2. The factors of the dividend are 32, 2}, and 7 5 • and
the factors of the divisor are ^ «, -OH, and 22i. Find th,^
quotient.
m
34 pHACnCAL PhOIJLEMS IX AniTHMETIC
''Si
1. Miiltinlv f) rd. 4 v<\ 2 ft. 4 in. hv 9.
2. \Vvi\o. in words (a) 1240. {h) Mr^i^ (r) ./,«,, (</)
4x7 11).
n. If I st'U silk at an advance of Wi % and jrain $0.2.')
per 3'd., what is the sellinu' jirii-c?
4. Divide 4S,") into fonr ])iifts that shall l>e to each
otliei' in ratios of .'5, 4-1, .">.', and (5 i'espeetiv(4y.
;"). The periniete" of a trianirle is 220 yds., and the
sides are in the V'ltio of 4. 7 and !). t'nid the length of
the longest side.
(5. A liai'dware merchant sold two stov.s for .$.'10 each,
piinini; 20 ' on one an<l losint^ 14H . on the other.
How much did the stoves cost him?
7. Three nnMi did a piece of work for Avhich they M'cre
paid Ji!.")4. If one worked (i hrs. per day tor 11 days,
another 1) hi's. ]>er day for 10 days, and the tliird 12 hrs.
per day for 5 days, how mnch should each receive?
5. A fruit pedler sold 41 oranires at 5 cents each and
(is lemons at 4 cents each, after which lu^ invested one-
tliird of his receipts iu bananas. Find the amcmnt paid
for bananas.
9. Make a prol)lem in which the interest, principal,
a?id time are given to find the rate per annum.
10. Express (a) .0007.") as a per cent. ; (h) 5 % as a
common fraction; (c) 127.302 in words.
11. At 22 cents a sq. yd., how much will be the cost of
plastering the walls and ceiling of a room Ui ft. by
14 ft., and 9 ft. C iu. high, if iV be alloweu for openiugs?
I'l{\( TKAI, i*|;(HtLK.M.S IN AlMTIIMKTK
1. A spccul.-.tcc soM I.JO simns railway sto,.k at 941
and invested the pro ds iii Imnk ."stock at I'.U;. pax in--
hrokn-atro ^ 7, Imth lui- .s.-llinj. jiiid l.uying. Hmv ,uji„'v
shaivs of tlie latter stock di<i lie Imy ?
2. The Eiffel tower at I'aris is :;oo metres hi.di Honv
many feet hi^^li is it? (A n.^-tr.. is ;j.n7 inc-iies nmre than
a yard.)
•'{. A man exc]ian<i:ed a pih- of wood 24 ft. lon^', G ft
liijrli, ami 4 ft. wide for 4.-.0() ll.s. of 1,mv at.+s.oir-i t<Mi
How 7nnch i)er cord did lie rec.-ive f..r liis w.x.dy
4. Exj.ress .101 of 1 II,. 5 ^z. as a decimal of I of 1 ,„•
22 l])s. 8 oz. ' ■
5. Simplify :
•^ (i - 1 -f (() /. )
:{
i)
()•?
I "f f of 2!,.
n'5 + ;,', of \-l ^ ,-, of ;!j|~^';;
n. Tw<. men, A and /.', a-reed to build a wall for -t.-JOO-
^l sent ;-) men 4 days, Ji ", m.-u for C days. How much'
"u^ht each to receive?
7. A s(iuare field contains 22 a<-res 2 roods. How h.ng
wdl It take a man to run round the l.oundarv at the rate
<»f 12 miles an hour? If the field he increased hv 9 acres
so as to form a rectani^le whose sl;orter side is the former
side of the scpiare, at what rati; does a man run who runs
'•<»'nid itinl mill. 8!) sec. h,n-er than was occupied in
running round the stpiare field?
«. If 1(100 laths cover 70 yards of surface, and 12i ll)s
of nads nail them tm, what will itcost to lath the (.."iling
of a church having the following inside measurennmts
Length 40 ft., width 24 ft., heiglit of si.le walls 12 ft "
height fr<mi the floor to the middle p<,int of the eeilin.^
-« tt. (the laths are nail.-d to ilie rafters) ? Labor costs
n^- I>''r yd., uails Gc. per lb. and lath $'^ per M.
30 I'ISACTK AL ]*|{«)H1-KMS J\ AiaTIIMKTlC.
1. Ill a lOO-vd. race .1 <'aii ])eat />' liv 4 yds.; in a
(quarter of a mile ra<'<' C can 1)t'at ^1 1>y 11 yds. ; l»y liow
miu'li can C beat li in a niilo race, sMi)posiii<; tliat
the avt'rajifo spt'«'d of cadi man wlitii riiiiiiiuf^ a
liundi-cd yards, a ((uartcr of a iiiilc, and a iiiilo arc pro-
portional to 9 : 8 : 7 ?
2. A certain star is five million nine hundred and
ninety-five tlionsand nine linndred and forty-fonr times
as far from tlio eartli as is the siin. State in words the
niimher of seconds which li^dit, travelling one hundred
and eighty-six tJionsand miles per second, will occupy in
coming from that star to the earth, if the earth is distant
ninety-three millions of miles from the snn ; and express
your answer iu years, supposing a year to eipial 3G5 days
6 hours.
3. Jacob, by contract, wa^ to serve Lal)an for liis two
daughters 14 years; when he had occupied 10 yrs. 10 mos.
10 wks 10 dys. 10 hrs. 10 min., how many minutes had
he then to serve ?
4. I bought of Poole & Thompson, Montague Bridge,
the following pieces of lumber at $12 per M : 12 boards
IG ft. long and 9 in. wide; eight 2x4 scantling IG ft.
long; fifteen 8x10 joists 14 ft. long; three 8x14 tim-
bers 24 ft. long. Make out a receipted bill for the above.
5. A dealer bought flour for $900 cash and sold it im-
mediately for $1080 on 6 months' credit, for which he
received a note. If he should get the note discounted at
a bank at G %, what would be the gain on the flour?
6. How many board feet in a stick of timber 36 ft.
long, 12 iu. wide, and 20 in. thick? How many sii-iare
feet in tlie entire surface of tho stick ? How many cubic
feet iu the stick ?
J'KAtTK AL J*I{()1JLEMS 1\ AlilTHMKTK'.
o<
i
1. A s<ni!iiv farm (M.ntjiins KiO acivs. Wluit is ihv
lfn,y:th of the iViicf tliut, siutoiiikIs it?
2. If tliodirtVn'iicc ii, liMK-lM'twccii twoplaiM-s is ;!lirs
lo mill. 1>() sec, ^vlmt is fl.,- ,litr.'ivii.-<. in l..iij;if ...1,. '
3. Fiiiu the nmoniit of a not,. f,,i- jfi'iLM, jriv,.|i July
lOtli, ]S!)4, and paid O.-tolH-r L'r,th, l,S!r>, lu-ariior 8 /
from date.
4. Find tli(> imn.l.(;r of s.j. ft. i„ tl..- sM-fa.-,. of a Ix.x
•■{ ft. V) ill. L.njr, 2 ft. :{ in. wide, 1 ft. 4 in. liiuh.
5. A lu-iiitcr used ;{ ivanis 5 ,|i,iivs 1!» slic-ts of j.ap.T
for i.rinlin.iT half-sluM-t posters. JIuw many did hv print,
allowinjr 1 quire to a ream f(.r waste ?
C. A farm has two of its four sid,-s parallel and two
not parallel; the distance l.etwe.'n parallel sides is 7(1
i-ods; h'ligth of non-parallel si.les, SO rods and llo rods
respectively. Find area in aeivs.
7. A man soM (I horses at $\:,i) v.wh -. ..n tlnve h..
-ained 30%- (,n the (.tliers h.st L'O '. Find oain or
loss.
8. .1 can do a piece (.f work in S=| hrs.. ,| and /; in
4.:, hrs., and A and (' in 4 Imiirs. Find the tim.-, if /;
and (' work toj^'ether.
0. .1 and B formed a partnership; .1 put in .^.'{OOO.
and at the eh)se of the first y.'ar added $2()<)() ; Ii put in
■t4()(K), and at the close of the second year took out
•f20()();^ at tlu; close of the third year the ju-olits amounted
to $34o0. What wa.s each partner's sliare ?
1 0. A certain lot is 80 ft. hy ] 28 ft. How many ] G ft.
hoards will be iv.piired to make a five-hoard fen.-earoun.l
It? If the boards are (i in. wide, liow manv feet of
lumber iu entire fence ?
38 PllACTlCAL PROHLEMS 1\ AuiTIlMETK
1. A solid wli«»st! luisc is 10 in. sciuun-, iiiul allitiuh! S
in., equals wlmt purt (»f a lO-iii. culu'?
2. If tlicfo aim 48 cliiMn'ii in a room 20 ft. loiijr, 18 ft.
wide, and 10 ft. liigli, liow many «*u. ft. of air to carli
child f
'.\. A waii-on ImmIv, 10 ft. lonir. .'5 ft. wide, and 18 in.
deep, ludds 3(5 1)U.><. of corn. If its width l>c incn-a.scd
in., how many hushcls will it hold? Il.id its hcij;ht
hccn inci-cascd .'{ in. and its width remained o ft., how
many hn.shds would it have held?
4. What is the wei<,dit of water in a full rectanj^'ular
cistern 7 ft. hy :{ ft. l)y 10 ft., if a en. ft. of water weighs
1000 oz.?
.'>. Divide $(>40 among J, /.'and (\ so that />* may have
six times as much as A. and (' \.\ times as mueh as />'.
(i. Find II.C.F. and L.C.M. of TJS, ;;S4, 7(iH, and 2:504.
7. Find the L.C.M. of all the prime nnndters hetween
2 and 17, inclusive.
8. A girl who attended school (iS days during a term,
was marki'd sr> 7 for attendance. How many days was
she absent'?
9. A man pays $'.]~7) a year rent for a house worth
$,")4()0. Will he gain or lo.se, and how much, in four
years, if lio borrows moiu-y at 7 % to purchase tlu'
1 louse ?
10. What rate of premium iloos 7 % stock bear in the
market Avhen the invesiment paA,s G per cent?
11. What is the net tax of a town whose taxable pro-
perty is assessed $4:50000 at 12 mills 'in the dollar, 5 %
being paid for collectiug i
i'KACTKAI, J'l{(»nKK.M.S IN AlMTllAIKTK
;{!)
i
IS in.
ici«;lit j
, how
'ciirlis
worth J
I
I four f
i
I
ie pro- I
1. A i.iun III vvalkinir tak.-s (Kloo sfrps in an hour- I,.,
ivarln-s (hu in-xt village i.i 40 imunWs. JIuw many M.-ns
< istant is the place? Uow many miles, if each Jtei, 1...
'2.7 teet? *
2. IIow many rolls „f ,,,,,„.,., each S yds. hn.jr ,,n<l Is
Ml. wi(l<.. ..•,11 ir.per the walls ..f n r„oMi l(i M l.y 14 It
I'.v 1(» ft. hi.h, ,le<h,etin- 174 s.,. ft. for windous and
doors '!
••!. 1 pun-hase u-,H„|s f,„- $.-,00, .-n,.! srll at the end of
nine months at an advan I l'o . K,.,.ko„i„u- i„f,.,,.st
iito 7, what was the real -ain p.-r cent, on the invest-
ment '/
4. January l.st a jra.s-meter r.iristered 11S00,.,| ft of
pis c<ui.sumed. AprilLst it r.-isten,! 14100 ,.,i ft \t
*1.7() per thou.sand en. ft., what was the .-ost <,f .^as used
in the intervening- time '/ "^
."'. A man having s(5000 on interest at 7 ', pavs >\^:UU}
tor the rent of a house. Would he gain or l...se, a'nd h<,w
much, l.y investing $4000 of the $(J000 in a house on
whwh he would have to pay a tax of 1l' mills in tlie
dollar, and $10 for watei- rent ,'
(k Miss Ellen Jones makes a dress for Mis^ Katie
Brown for which she furnishes tiie following materials •
() yds. percaliuo at ISc, 2 yds. sih'sia at 2r,e., .i yd ,n-a.ss
cloth at 14c., f yd. velvvteeu at $2.00, 4 yds. hair cloHi at
4oc., 3 spools silk at 8c., I spool thread at 4c., 1 spool
twLst at r.c., 5 yd.s. cord at 5c., 1 pr. .shi.'ld.s, helling l->c
I doz. l,on..s r>4c., .-, yd.s. casing at 4e., 1 pi,-..,. |,i„aing
nhhon iSc, work $11.00. Make out Miss Browns l.,ll
and receipt it.
4i) rUAlTK Al, I'koUI.KMs IN Alii IIIM K I 1< .
1. If .',■; <»f 'A\ tiiiHs 1 Ih' imiltiplit'd liy I, tlir prodii.-l
divided l>y fj, tln' (|uolicnt iin'i-ciisrd liy 4.'. aiil tlic .sum
diiiiinislird l»y -, of itsolf, what is the rnimiiidcr?
2. I liuld Mr. Hlak.-'s not.- for $;{(;(»(», dated .laimary
Stli, 1S!)(), due ill tint ycMi- williuiit iiiti'i't-st. What is
till! ca.sli vahu- -Iidy L'ntli, iS'Mi, uK.n.'y Wring worth G / ?
;j. A cidn' iniiiKrsfd in a rcrtani-Mlai- reservoir :U» in.
h>iif,' and Ki in. wide raises the water :5 iiu-hes. What i:^
the ed«i:e of the flllie ?
4. What nuinlter increased hy J."» ' of itself e(|iials
',•_*(»(>? What nniiil)ei- diniinished l>y 17.1 of iis(4t
equals ;{().:;■:' 1 ll2 is 140 / of what nuinlier? (iO / (»t
what nuinher equals *J<i?
; \ reservoir supplies a town with 4.")7-')'^<K) ^-aUons ol
water daily. If its surface area is 7 acres, how much will
the water be lowered in it, providing' one-half us imid
i-uns ill as runs out ?
(I. An ugeut iu Toronto sells 4r)(H) bus. wheat for ni»
at ()4.ic. a 1ms.; the proceed:- he invests in wool at 1<h,
lb. If his connnission for sellinji- the wheat Ite \.\ anii
his coinmission for buyinjr the wool 2 /, how many lbs
of wo(»l does he buy for Tiie ?
7. Find the present worth of th<! following note, Juni
ISth, 1S!)(>, discounted at the bank, rat<! of discoun
being G% :—
$:5'2().()0. ChaHottetown, P.K.I., Feby oth, 189(5.
Six months idter date, for value received, I proiius
to pay W. W. Stetson, or order, three hun<li-ed an(
twenty dollars. Ci. J. MeCin-mac.
S. From a lot of land 40 rds. sipuire 1 sold 40 sc^. ^d^
W^lmt is the renuunder worth at $45 au acre?
riJAtTK Al, J'koIJLKMn IN A I.ITII MK T|r. H
V .Slim
inimry
'hilt is
1 (i / ?
:Ui ill.
^'Iiat is
(•(liials
f itself
% of
Ions of
icli will
< llMlcll
for jn»'
I, Ku.
U and
luy lbs.
(.', June
iscouut
1S9().
[troiiiise
■('(] and
i-inac.
!>([. rds.
'• ^^'^^ It a hill of ^^..ods lik.ly to 1... |Miivl,as.-d at
a lianlwarc sii.n-, jind n'<M'ijir, i-ayiiK-iit.
2. A H-hoolhoiisr isinsiiiv.l for;{yi-N. a|. I.] piviiliim,.
which is $(iO; il„. iusiiraiiro valiiafioii is j,' '<>i' th.- n.st ..|
th.- hoiis.-. What is th.' undi-rwritri--s loss if it hiinis?
.'{. Alaiidlonl owns L';{(»4<» a,-ivs „f Imm.I i„ thr fun,,
of a sqiiaiv. How iiiurh will h.' hav to pav a snm-vor
to lay it oat into h.ts of Kid ;„.,vs .,„.h. if lir has to {,av
+1.1.'.") ftu- i-vi-ry mile run ?
4. I have .tLNMIO „„ i„|,.,.,st -M (1 . \V1,,„ ,,,„„ ,„„^,
1 invest in S ^ hond.s, .s.Hii,^- ..,t !)s, to yi.Jd llic ^.•,„H.
annual income?
.'). A lanihei-man owns 74S(; Mcivs of timiMiv.l I.hmI in
the form of a, .sq,iare. How ,„,,,,y „iiles aionnd it ?
fi. The distance f,-oni ("harlottetown t.. S,ii„„ie,-.side is
<■><» mih's. At $1 ajac-e fo,- posts and 7.-. a II.. to,- wii-
what will the posts and wiiv for u tch-phone line cosi
If the posts an; set oO yd.s. apart and a 11.. of wire
stretches ,")() ft.?
7. A room floor contains 4:{L> s.p ft., and its breadth is
t(» Its len-th as ',i is to 4. What are the .liinensions <.f
the room ?
S. How many barrels of flour at .+4 a l.anvl shall an
Hp'iit s<'ll so tluit lie may remit to his princii.al .t-Jold,
after dediictinjr a eomniissiou of 2.\ ' ?
!>. How mudi will it co.st to paper the walls and ceilin,ir
of a room 04^ ft. lonir, -M) ft. wide, and 10 ft (i in hi'di
.•It 27iie. a si[. yd. ? ^ '
10. T)educt ^ of ,: from ii of Jjf, ad.l to il„ ivmaiinler
,0, divide tlie sum by Gi, aud chauge to a deeimal.
\'J. VHMT\i\\. l*i;n|,|.K.\LS IN AuiTllMKTir.
1. A mail (Inw :{() ' of liis l»aiik «l.|M.sits himI s|mii1
'2't ' of tlif iinnny (Ir.iwii to imn-liu.sc u ln»rsc for !i*!l7.>0
Find how imu'li ho hiul in the Imiik JM-t'oiv ilniwiiivr.
•_'. Kiiitl IIm- fact! ot a !)0-(hiy iioto that wlu-ii di-s.-ouiitt-d
ait 12 ' will pay foi- 1:{7'^ yds. «'loth at %'1'\ a yd.
:{. An-a of till) ^alili' end of a house is ;{7s s(i. ft.
li-ii^'th of liasr, 14 yds. Find lui.t,dit of ndj^c
4. A niinc-ovviM'i' iiiado a contnu't to dtlivor 1<>U(K
Ions of <-oid ill 4 inonllis, I'lnployin}^ ;')()() iiicii to j^i-t i'
out ; at Ihf fiid of :{ inoiitlis, with only :{<H»0 tons dii-.'
4.")(> nn-ii struck. How many must he advrrtise for t<
fullil his contract ?
.'). Find the time of day if % of tin- time past midiiififh
e«|uals tiie time to inidiii<;lit nuain.
(■». Mv n<"vnt sold in Montreal 10(10 l.us. of wlieat
commission 2 %, at S4«- ; invested proceeds iu doth, com
mission 2 %, at S4c. a yard. Find number of yard
iMiujrht-
7. Fxi)ress by Arabic ii(»tatioii twenty billion, niiieteei
thousand and nineteen ; by l{<»miin notation six hundre(
and live thousand; in ti.iruves, MDL; in words, ()•_»:>()•-•.').
,s. Add ,Ia expressed decimally to G<M) and twenty
five teii-thonsandtlis; diminish the sum by HiX; .,'„',;„ c.n
jiressed decimally; multiply the remainder by (I and .'J-1
thousandths; divide the product by six thousand an^
thirty-four ten-thousandths.
!». Divide ;57.') by .7."» ; .7-'> ])y ;}7.'). Find the i>rodu<'t o
their quotients ami express the answers in words.
10. If (I m.'ii di^' a cellar 22..') ft. hmi?, 17.8 ft. wide, an
10 ft. a in. deep, in o days <.f 10 hrs. and L") min. eacl
how many men will it reipiire to di^' anotlior, in 12 day
of S.2 hrs. each, 1.") i"t. long, y4-;| ft. wide, and 12.8 f
dee^> ?
cx-
ri;A<Ti(.\i, I*i;miu,k.m.s in AitrTiiMi.nr. |;;
^ 1. How iriiK-li will it <-usf f.. plnsNr n mom M\ ft <) j,,.
Iniijr, 14 II. S in. wicl.-. uri.l |i( ||. (I m. Iiitrli. il' llinv ••iiv
tliiv». windows (; n. I.y -J ft. !» in., two .loors 7 It. l.y :{ ft.,
aiMlul.a.s.-lM.nnl I 11. wi.lc ; tlu- prici- of |,lii.st,-nuj; l.riiif.r
-*•'»(', a sqiimt' yard ?
I 2. Iinm on-liai-d. •] of tli- tiv...^nn'a|.|.lc.tn'<vs ,'„ |m.,i.-I.-
(•••■•■s, and th.' ivmaindrr |M-;ir-tivs. whi.-l, .n-, l'(» „„,rv
than 4 (»f the wliolr. Mow many iir.s in llir oivh.-inl?
."{. A liavinjr a farm of l(i!» .•„•.. wlii.h iviits for
$nsi.L'.-), sells tlK'siiinr forjfslL':. ,in a.-ir. iind inv.-s; , ih,.
pi-ocfcds in Dom. of Ciina.Ia (. ' nt |(»s.«, hrokn-iiMv j
for puivliMsinir. Will his yearly it me l.e increased (»r
diminished, and how much ?
4-. A man havin<f a sp.in of hoi-ses for sale, ofTere.)
them for $4X0 cash or a note <.f i^:,:,(\ ,hw in I \ r. s mo.
without interest; tho hnyer aeeej)|,.<l tl,,. |;,tt.r oiler. Did
the seller jrain or loso therehv, aii.l how mueh. interest
iK-iufjT G % ?
5. A fruit dealer l)on«rht oran^'es :it the raf.' ..f l.",.. |„.|-
• lozen and sold them at the rate of ;{ for lOc. ; I, is prolii-
were $72. How many l.o.>ces of 24 do/.. oiiniLrrs -iieh did
he buy!
^ r». Tf a farmer uses 1 p(.uiid of fertili;cer ..ii :; j.ie.., of
irround 2 yd. .stjuaiv, how miirh will he us. ..n
aere ?
<'> an
7. Tf it eost $42.") to feneo a fi^ld 72 rd. hy 0>! rd..
what will it eost to feneo a square field of t!,.' s iue ar.'a .'
8. "What aro the eonteuts of a loj; t]C) ft. hin<r, IS in.
in diameter at the smaller .rid, and 24 in, ut the' l.ir^^vv
end ?
44 rUACTK AI. ruolJLEMS I\ AhITHMETIC.
1. Ill a sciuiirc fi(4(l <'(»ntiiiniii_<r 1;, acres, li«nv far is the
ceiitiH' from eiicli corner, uiul from the iniddlo of the
side ?
2. Divide 109 nils. 7 fur. 29 rds. 7 ft. .'} in." by 4^.
3. H<)w iiiaiiy days of 7 lirs. eaeh will it take a man to
travel ;J9() miles, if he goes ]'■]() miles in 15 days of 14 hrs.
eaeh ?
4. T rented a house at 7 /' of its value, and in 9 mos.
18 days I received $122.08 rent. Find the value of the
house.
f). Find the face of a sight draft costing $70.40, when
exchange is 2^ %.
0. A deht of $53.9.") w;is du<^ May 21st, 1S80, but
settled Novend>er 9tli, 1874, at a discount of G %. How
mucli money was paid ?
7. Find the side of a square field ecjnal in area to a
rectangular field 07(5 yds. long by 2r)G yds. wide.
8. How far from the house must the foot of a 2r)-ft.
ladder be placied to reach the eaves, 2'-i ft. from the
ground ?
9. How much cheaper would it be to pave a street one-
fourth of a nule long and GO ft. wide witli asphalt at 22c.
per s(|. ft., than to pave it with granite blocks at $.'{.10
per s(i. yd. ?
10. For what sum must a cargo of goods valued at
$12:?G0 be insured at l'| % to cover both property and
}iremium in case of loss?
11. What is the distance from the lower corner of a
room 24 ft. long, 18 ft. wnde, and 12 ft. high to the
opposite corner?
Pkactkal Pkoulkms i\ Akitiimktk . l-*)
l>ut
1. Make and solve a i>rol)]om illusfmtinj? tW i\\)\)]\.
cation of s(inaro root in ftndinjr the side ot a ri^dit-anirled
triiingle.
2. Wlmt will it cost to plastiM- tlie walls and ceiliix' of
a room IS ft. l<,„g, 12 ft. wide, J) ft. hi^di, at 4()e. pcr's.,.
yd? IL.w many cords of \v(K)d wonld the room hold if
completely filled ?
..Simplify I 1^- "■•■•, '"-".« „YK,, J.
4. A boat whose rate of sailiiii,' in still water is 14
miles an hour, wasaceeh'rat.'d :].\ miles ])er hour in iroinj:
down stream and retard.-d the same distan.M' in (..miinrr
up. It was 4 hours lon<,'er in comiii<r up n certain
distance! than in going down. What was the distan.-e ?
'). If a man buys a ton of potat(>es for $15 and sells
them for l.le. a jK-ek, what is his gain per cent. ?
G. A druggist bought 1200 ]l,s. of alum, avoirdupois,
and retailed it by Troy weight. How m.wiv more lbs. did
he sell than he bouglit ?
7. The rent of a sqnare field at £2 14s. Gd. p.-r acre
amounts to £27 r,s. Find thr ...st of i.utting a paling
fence around the field at 9d. a yard
H Simjdify
} of a - m of m ( W M
^ - 4
(
0. If a mixture l)e made of ll)s. of candv worth 12c.
a lb., 7 lbs. at Uic. a 11)., and 4 ll.s. at 2()e." a lb., what
will 1 lb. of I he mixture Ix- worth ?
10. A sidewalk is l.-)0 ft. Ion and 4 ft. wide; it is
nmde of 2-inch plaidv, crosswi.s,- on 4x4 sc:antlmg.
Find tlie cost of the lumber at $24 per M.
46 PlUCTICAL PnoBI.KMS IX AuiTlIMETIC.
1. Goods l)oii<;*lit. at 40 % and 10 % off wer«^ sold at
12i % abov(^ list. If tln' lucrc'linnt's expenses are 20 % of
his sales, does he make or lose, and what per cent, upon
his investment?
2. A farmer's wlieat crop averages, per acre, I of -svhat
his oat cro];) does, Init Ik^ receives i30 % more per hnsliel
for it. If he receives !|!l.S(K) lor his entii'c croj) of GO ac.
of oats and 40 ac. of wheat, lind the value of an acre
of wheat.
3. I bought a horse in Liverpool for £;>() 9s. 4d. and
sold it in C'harlpttetown for $K)4.7r), paying £0 2s. .'!d.
freight. What was my gain or loss per cent.?
4. Find the number of revolutions made bv a carriage
wheel 41 ft. in diameter while passing over tlie road
from Georgetown to Cardigan, which is G mi.
T). In a school of 28 scholars, 3 j)upils are l.lj yr.
old, 4 others of 14-,', 3 of i;5,\, 5 of 11. \, G of Or, and 7 of
S|. Find the average agt» of the scholars.
G. Wiiat per cent, of 904 must lu; added to that
number to make the sum lOOG?
7. If the unit of mcasui-emeut be f; yd., what is the
measure of 3J in. ?
8. Express as the decimal of a week the time y<m are
in school each day?
9. The Belfast Railway ran across a man's farm of loO
iu\, which is 1;^ mi. long, and took a sti-ip 24 yd. wide,
for whieh the company paid at the rate of $45 an aere.
How^ much did he receive ?
10. How far will a mower be drawn in mowing a square
7-acre field if the mower cuts a. 35-foot swath ?
VUA
(TicAL Phoulkms JN Ak'ITIIMKTIC. 47
1. Multiply 4!, l.v 7; mi.l ,livi,l,. ;f\ l,y ^ ^\ . ,„„j
fin.1 tl.o <liff,T,.n.... lH.tw,M.M (1,,. HMu mnl .liffi-n-un. of
rhcse rcsiuts.
I 2 I^i,„| ^^ ^^^,^^. iMi.hvny l..lu-,M.n (^„,m.„ Vi.tonn's
: iHi-tlidiiy and Clifistiiiiis.
^ n If ,t...k bought at OS^ ,nll pny (!{ / .„ tl.. inv-st-
I ni.-iit, at, wliatrato should it 1„> huw^ht !<• pay S ?
I 4. Exp-o^ .V of lis. lid. + /'. of 4 .uiui-as + '. ..D of
*■■+ - IS oi 'A<i. as a fraction of £1!) 4,s. 6d.
i 4,-N':i-r';^' '""V*^ '-■•^«lv'"<"M-y will ..,„H...l a d.I.t of
I UH4..A), du,> ,u .{ u.o. L>0 dy., u,(„M.y L.-ino. ^oHh r,.i /
I per annum? " - /"
I Mid San ^, .„...,..<, 4:^ d..^n...s 2/^ ..in. Mvst, ;ha
. ^.no w.ll ,t ,. in X..V York wlu. it is u.x.n nt S
I hrancisco?
J 7. A jounn-y of HfiO „d. was nnul. l,y vail, stoanior
jj.nd..a.4.. Tl. distan.. l>y ...h was on..fou..th and
l.<. d.sta.uv by s.a tlnv,.-fourths of that hv rail Tla-
I ^'-e I>- 'Mil., by ..<^,.h was double, and by s^, four-flf,hs
I of that by rad. ^\ hat was th. .^xpenso of tho wholo
jnurnoy, radway fare bcin^^ l.r.7142N,l. j.er n.il,>?
S. IIow many onbic iWt in a ton of i,.,-, ifa <^•d]on of
,-t..r weighs 10 1b., n..asun.s 277.274 ... ^
I ''xpands on.'-tonth in frci-zini:'
I 0. How many half-crowns are thr.v i„ n7()o jr„i„eas ?
, m I invest. o<{ual sums i. ,4 .toek and in a ;] 7
90. \V hut IS the j.riee of th,' .{ p,.,- ,vnt,sf
4S I'UACTICAIi I'UOIJLEMS 1\ AlJlTIIMETK".
1. Sinii)]ify {a) :!.4i6 + l.OolOi - .24<'i7<"t ; (/>) divid
.'57.4;j('i by .l;5!'t.
2. A sqiiai-o field contains 8^ ac. p^'ind tlio cost o
niakiiiir a I'atli tlirco yards -wide inside tlie field, ronnt
tile Itoiindary, at .'i2<'. per S(piare yard.
;}. Snlttract ..-'{Ts of Is. fi^id. from .37n of 2s. {)d.
4. A snin of money is to lie divided anionjjf 11 mei
and ]S boys, and ') men are to i-eeeivo as mneli as !
boys. "When 3 men and •'{ boys luive received tlieii
shares, wliat fraction of the whole sum will renniin ?
"). Simplify:
(2-' 400 , X
.,: + ,- - U of ;i> ) -f- -y,\ + } of ui„ + ,^
C). Find value of ,'-, of £1 + ^' of Is. + ..'\ of a fjuinei
+ V of £1 (Is. Sd.
7. The circTimfereiice of the earth is 40000000 metres
the lenyth of a metre beinj,' ;{9.;{707!) in. ; calenlat*
the diameter of the eai'lh in miles, assnminj; the rati(
of the cii-cnmfereiice of a circle to its diameter to Ix
;{.V) : li;!.
*
H. A watch, set on Fi'iday at 9 p.m., ^ains 4.1 sec. ii
12 hi-. ; what time does it show on the ne.xt Monday a
.'> i).m. ?
0. Wlien silk is sold at 10 francs 25 centimes per metro
find the eorresp()ndin<,' ]>rice ])er yai-d in .shillini;s an(
pence ; snpposin<r £1 = 2.") fr. 20 cent., and 1 metre =
:U).:}71 in.
10. Olttain tlie en1)e root of 10.01 and the sijnare rooi
of (501 ;>.">.,')! 71 S4."), t(> T) jtlaces of decimals.
- riiBif . ■•.-:> -iKi V. csarvi
it-i^i.V 1-
I*KA(TI( AI. PlJOIW-EMS IN' Ak"
ITIIMKTK
41)
1. Tu-o cojr-wliools, one with 15 t.'otl,, tlie otlior witl,
18 tet'tl,, w„rk togotli,.,-. If the funuw t.m.s round 1(1
tn.H-s m 7A .s,-,... ],ovv many times will tlio latter turn
••ound in 21 see.?
2. An en-ine while driving machin-rv ])urns ooal at
the rate of 1 ton 12 ewt. 2 qr. in 8 1.^40 n.in. Wln-n
j thenrnvhineiy is not in motion, the consnmpti.,n <,f eoal
I IS only ,', of this cjnantity. How mneh e(»al will tiie
I "Mjrnie b,„-n in V>H4 In-., during i- of whieh time the
maehinery is at rest f
•i. A and 7? ride a raee of ,31 mi. on Lie voles The
d.ning-whe<.l of .t's maehine nmk,.s .'{410 revolntions per
iK'ur, and has a cireumferenee of 1(58 in.; that of li
makes a:,20 revolnti<.ns jvr h(»nr, and has a eirenmfer-
''»<••' «.f ] r,2 in. Which will win, and l.y liow mueh ?
4. Add togeth.T ..']()2r, of £0 7s. fid., ]..3fi28 of 10s., and
■<»<'<4 uf 10(1., and expre.ss the an.swer in francs and'een-
tnnes(l franc = Oid.).
5. An Iri.sh aei-e is to an Engli.sh aei-e as 49 is to 80}
I1..W many English ac.res are th.-re in a farm <.ontainin-
«.)2i Irish acres ?
n. If a certain amount of worlc is done ])v 9 men l'>
women, and 1.3 hoys in 11 dy., In.w long will the same
work take if 18 men, ,3 w.nnen, and T, bovs are set to do
It, a.ssuming that tlu* ratio of a man's w.»rk to a woman's
IS as ,) to 3, and a woman's work to a boy'.s as 4 to 3 ?
7. A piece of timlier 15 in. square at each end, and 15
J t. long, is to be measured. Find its <'ont,'nt.s, and how
tar from the end must it be e.it across, so that the piece
ent off may contain 1 solid fo(»t?
50 I'l.'AC TK Ah Pl.'olW-K.MS IN AuiTII.MKTIC.
1, TlKTc is a tri!iii<ruliir ('(tnificld avIiosc sides are la
200, and 27)0 yds. Find tlif nimihcr of acres coiitaiiM
in tlir field, and tlic cost of rcapiiif; the corn at $1.!
per acre.
2. Make out and receipt the following invoice :—,*](
oniniTcs at lO^d. per dozen; 12.")0 apples at f) for .'M
2.")00 e<;,i,'s nt 9d. for 10 e<;^rs; KJboxes figs, each 511).
oz., at 7d. per p(»und; 8i sacks of ])otatoes, each,'] 1m;
at 4^d. per gallon; 5 gal. stra wherries at r).\(\. p(
quart; H score i)ounds potatoes at 5 Ih. for '{^,d.; 2^11
tomatoes at lid. ])er ])onnd ; 2'/ jik. peas at Is. iul. pc
peck ; 7~) eggs at Od. piT dozen.
n. A gentleman has a garden in the form of an eqnih
teral ti'iangle, the sides of which are each 50 ft.; at eae
corner of the garden stands a tower; the lieight of tl
tower A is no ft., that of li 'M ft., and that of C 28 ft. .^
what distance from the bottom of each of these towei
must a ladder of .same length with each side he j)lace(
that it may jnst reach the top of each tctwer?
4. Wliat are the contents of 27 hoards, each 1.'} ft. Ion
and 18 in. wide ?
;■). There is a meadow of 10 ac in the form of
square, and a horse tied ecpiidistant from each corner <
it. What must he the length of the rope that will jx-i
mit the horse grazing over every i)art of the meadow?
G. The largest of the Egyptian pyramids is 800 fi
square at the base. How long a road. 4 rd. wide, woul
occupy as much hind as the ba.se of the pyramid?
7. The letigth of a rectangulai' iichl being 2.") chains
links, and its breadth 14 chains 7'") links, what number o
acres does it contain?
I'KA( Tl( Al, I'ltOlJI.KMS IN AlMT
II.MKTIC.
I
1. Ill u l.lock ..f L>.-, hcMisos, cm-h lKMi.se 1ms 17 win-
dows, I'l.cli window 4 iKui.-s, .'.-Ml ,.u..h imno uwnsnrvs
IH m. hy «J in. What will lu- th.r cost of glazing ull tlu-
windows at Gd. jht sqnarc foot?
2. A m-tan-ular cist.Tn lOi ft. in length, GJ ft in
l.ivadth, and '^ ft. in depth, contains 14()^ cu. ft of
water. What is tht. least nnniber of bricks, each 9 in
longl.y4Ain.widel,y;nn. thi<-k, that must be timnvn
into the cistei-n to mukv tin. wafr rise to the top, a brick
iH'ing found to absorb Avater to the extent of '- its
volume?
'i. Express .-,()()();{();] farthings in £ s. d. and subtract
the result from 10021 guineas.
4 Two acres of land aiv t<. be cut from a rectangular
held whose wi.lth is 2 chains fX) links, bv a lim^ paraUel
with either end. What is the length of the plot?
Jk a 9-months' note discounted at (J % yields $477.25
Find the face of the note.
fi. If stock bought at 92 AviU i>ay 7 ;: on the invest-
ment, at what rate should it be bought to pay 10 "^ ?
7. A pil,> of wood 128 ft. long, 4 ft. wide, and 3 ft
S m. high, is sold for $:].; '» a cord. How much money is
received for it ?
S. An agent sells goods for his firm, paval)le at th,-
tonowmgdat.'s:-$;20du.' 7tli .lanuarv; .fl.-JO due 9th
February J $-200 du,> l.lth .March; $.-,()() due 20th May
$240 due ir.th August. Find the average time of
payment.
9. A room is 14 by 1 ft. l^luit wiU it cost to carpet
the fioor-eai-pet scAved and laid at 90c. a yard— i^
9 m. ar(> aUowvd for matching, stripes laid lengthwise
earjjeting ^ yd. wide?
02
1*I!A( TK AI. TWOULEMS IN AltlTlIMKTK .
1. A owned il (»f a fiictorvuiid sidd '} of liis sluirc to /
wlu) sold A of wijiit lie lioiijifht to i', \vlio sold H <»*' wlm
lie l)ou«rlit to />. Whiit part of the fuetoiy did eueh <
them own ?
2. A note for $.■)()() dated October 17tli, 1S{)0, was pai
April 12th, 1902, with interest at G %. What was th
amount i»aid?
'? A ball disehnr«;ed direetly ui)wards returns to tli
earth in IG sec. How high did it ascend?
4. A man travelled northward 24 mi., then enstwar
HG mi., then southward 10 mi., then northward 4 m
How far was he then from the starting point?
5. What is the face of a di-aft due 90 dv. after si<di1
with interest at 5%, which can l»e bimght for$lH0,S.2
when exchange is 1^ 7 pi-cmium?
G. A druggist purchased 9'| oz. of <iuinine at 40e. ai
ounce avoir., and sold it at (JOc. an ounce troy. Ho\
much was his profit?
7. Find t-ost of 4 ac. .'{ ro. f) po. of hind at $Gr).r)0 pe
aere.
8. A tree 140 ft. high is in tht! centre of a circula
island 100 ft. in diameter; a line G(K) ft, long reache;
from the to}) of the tree to the further sh(»re. What i
the width of the stream, the land ou each side being o
the same level f
9. Find the cost of a 4.")-davs' draft for 83800, diseoun
S%, interest 7%.
10. If 20 men in 10 dy. of 8 hr. each dig a ditch 150 ft
long, 4 ft. wide, and Jl ft. deep, what length of ditch 3 ft
wide and 2 ft. deep could be dug liy IG boys in 12 dy. o
G hr. each, if a boy does only half as much work as i
man ?
I'KACTKAI. I'kOlJLK.M.S IN AlMTIIMKT
ir
').)
, 1. If 11 jxTsiMi loiiiis 111,' $'2r>{) for S in..., f(.r li.,w loiijr
ii time must 1 hnm him !ii4()(> as uu tMiiiivalciif ?
2. IT<»\v many s<|uaro yards were tlicro in tlic area of
Solomoir.s Tempi.', whose (iim.Misions an- m.-iiti..n.-.l in
I. Kinj;s, eluip. vi., r.'.-k.Miinj,' (li.' enl.it to l..- is in./
I Tf N.mh's ark was .*}()() cubits l.)njr, .">() wi.l.' an.l ;)() high,
how many euhi.; yards did it contain ?
^. On.Mjuarter acre of frround is .'..v.-r.'.l with \v...mI
I'iled 12 ft. high; how much is it w..rth at $;}.2.'i a cord !
4. B(mght $070 hank st..<'k at 4 per .vnt. advan.v; s..!d
at a discount of '2.\ ]»er cent. Find the h..ss.
5. The sides of a triangular h)t arc ]l.")i ft., 12S.\ ft.
and r.iVl ft. respcctiv.'ly. Il..\v many board's will it tak.-,'
and what will it cost to fem;e it with lumber at .$7^i [..'r
M., tlie h)ngest boai-ds p(.s.siblc being used and the fenc.-
being r> ])oards Ingh, the bott..m one 10 in. wide, two G in.
wide, and the others 4 in. wide?
_G. I have two pieces of cloth, ea.-h M yd. l.>ng; one is
-•'* % hmger than it sli.iuld be, a" ' ' -ther is 2.") 7
shorter than it sh..ul<l be. Whut w.>Mi 1 be tlie .•.)mbin«-.'i
l.-ngth of the two pie.'es if each ^^•ls of the i.roper
length ?
7. Copper weighs f).')!) lb. and tin 4(i2 lb. t.) the cubi,;
foot. What is the w.'ight of 1 .mi. ft. of the mixture con-
taining G parts of coi)per and 3 j.arts of tin ?
8. A note dated January 4th, 189."), for $9874.69 with
interest at G %, had the following endorsem.'iits :— July
l«t, 1895, i-eceived $.-579.28; Feb'y 18th, 189G, received
$4.)8.74. What was duo on the note Jaiiuaiy 1st, 1898 ?
"Jl riCACIKAl, I'lJoni.KMS IN Al.'ITll.MKTlC.
1. If it cost .tU to i.aiiit tln' walls ami wV .i^r <,f
rooiri !':» ft. l.Mifr, L»() ft. wide, ami 10 ft. Iii^r],^ li.,\v' iiiir
will it «'ost to i»aiiit tlit; walls ainl eciliii},' <»f u room 50
loiij,', 40 ft. Avidc, uiul 1*0 It. liij,'!!?
'J. Two men start from the snni) \»n'\t. Oiu! tniv«
•■{() mi. (Iik; north and the other 40 mi. duo w.-st
tlu' saiiK! tinu', aiud tlit-u th.-y l»oth turn and travel t
wards cucli other jit their fortner rates of speed. WIk
fiiey meet, Ik.w far wll eaeh luive travelled from tl
comm«m startin<,' jtoint?
-\. 9 lir. G min. S see. is what j.art of l:{ lir ;i!) mi
12 sec?
4. Fin<l the exact interest at r> / per annum <
$.•{12.7.'), from S.'ptemher 11th. liJOl, t.» Xovemher 2;{r
1!)01.
.'). Find the cost of a stair carpet for a fli«,'lit (»f ]
steps, 7i in. ri.so and 10 in. deep, at (iS cents a yard, tl
steps to include U in. tloor space at the top of tlio stair
G. Aph)tof land 200 ft. wide ca- »e exactly dividt
into lots 42 ft. fi-ont, 4S ft. front,* .)() ft. fn.nt. IIo
many feet in lenurth must the j. ,; necessarily l)e i
answer tlie.se conditions?
7. Find the value of
*t I , Ol _ , ,
;\ + (2;; of 1,\) - i;l (:i-\^ -^ z\) +
]r^ of
.1282.-) 4.2 l(i 2.t
8. If I piircliase D. A. R. G i)er cent, stock at 99.J
brokerajre J ])er cent., and at th(> end of fi mo. sell it i\
I04i, })rokerage ^ p«T cent., what per cent, do I mak
on my investment?
1« .
J*.i.V(Tl( AL l'l;n|!|.|.;.Ms | .\ A I.I TIIM i; n,
■ »•»
•ig of a
>\V llllK'll
till ')() ft.
V. Iniviils
Wfst ill
j'uvcl 1<t-
W'hcii
'n»Tu the
•>l) mill.
iiiini on
<vv 2;Jnl,
it of IS
iird, tlu'
o stuii\s.
divided
t. How
Y l)o to
1. Tlif iiss.'ss.-d valiiutioii uf a s<-li(.u| ,i
»md Ji tax of !i(ll,-) upon said <li.st
iiiiiiiial sfliool nifct
i>tri.-t i-*'j:;()(i(»
iK-t is v..hd al III
iiijr. Find tin- t
'>^ "II .1 farm
J asscsstd fMi- !f<i(i;io in ^,,,1,1 aistHct.
■ 2. Find til., snm of 2^,... 1 „<•. !):!} >.,, ,..|. and ;!(; s.,
I rd. IS s(j. yd. '
••{. Til.' n..t pri,.,- of an artiVI.-, alt.,- .Irdii.iiii.^ ,|is
.■oiints of ;{;;,■ 7 „n.l 2:. -; fn.m tl... list ,„-i,.,.. u..,s $4.,s7..
What was the list pri.-.' ?
4. Til.- i.roc.M.ds .,f a 4-montlis' nut., nia.lr an.l ,lis.
••••nut...! at liank of X.,va S.-uiia, An-nst Hih, ]'.Hi] ..,1
<;% Iter annum wr.. $22.-».4(». Fin.l th.- f.„-.- .,f ll',,.
IKttc.
' - 1 7
at 99^,
H'U it ut
I make
•"». A m..r.'liant sold a <|naiitity ..f ......Is fur ^')H\r>
.in.l th.-ivhy l...st = of what th.. -.h.,|s ,.„.st him. Fin.l
tii.ir (•.»st.
I (•>. A has )f;y an.l /; .^7, with whi.-h th.-v l.uv a JM.at tor
I *!.). (' ^av.. slo f„, . i,„,.,,.,t i„ ,,,,. 1,,,^;^^ ^^..jj^ ^1^^^
I nmU.rstan.linjr that .-a.-ii ..f th.-ni shall ..wn ..mIv I .,f th..
I lM.ut. ll.,w nm.-h .,f th.. $1(1 r...-.-ivod from (' h.-ion-s t..
I -4 and li<»w nin.-li t.. /.'? "
7. Divide, th.. snm .)f .1 and .u l.y .1, and |„ fl„. ,,.snlt
add .()(K)7. Divi.l.. th.. .-.■.snit thns „l,taiii...i Lv th.-
<litfer(.ncL. ])..tw(.cn .Ifi.^SlJ.j^ jind 4;{.;]r)7;ju.
S. Find my annual in.-.mi.. from an inv.-.stm.-nt ..f
$4.>4,>.75 in i>,ank ..f P. F. I. 4 :' st.M-k at 119.1, hr.,k..r-
!). Find tlu. altitn.l.. of a ri-ht-an-l...! frian-l.^ whos,.
I hypothenus.- is .'{(Ki ft. and h.ts,. ;{(;(» n.
10. The princii.al is $9;J0, tlu- iutt.r..st is .$n.-,.;]2 an.l
tile rate is (i . Fi,i,l tlu- tinir.
"66 I'lar-n, Al. I'l.oni.K.M.s in AlilTIIMKlic,
1. \ Ciirin.-i' piii«l .t47.-jr. iiisiinuirr i.ninim.i ..n
I'-.-i.i r- ,rs..s. tl... nih- iM-in^' 1 j /. How .niidi was I
2. ' of \vo<m1 (i;! ri. innir, 4 ft. ui.Ir, s ft. i,i^
>v -^ I nio u cord. l-\.r h„w irm.-h was it sul.l?
•'■ I '-'. .111(1 (• trail- ill |.ai-|ii(.rslii|,. .1 furnislics
the -a) .: ami i; to liavr i uf tlic ^ain fuv «'Xt
>«'i-M.. V /; uml (' f'M-iiisli .f.-iiKMI racli uii.l flic ,^n\n
$:)7(i'i V'!,'* .- ' .siiaivufrarliy
^ ^' -^ ' »' 'i ^vhat will itcost, to iHiiM til.' w!
of a . •llai- J I < . ,,nir. IS ft. vvi.l.., an.] r> ft. a.'..p, tl
wall ,n in 2 f:. thick Jiud to <'.\t.-ii<l :\H in. uhovJ tl
j^roiiiid y
.'.. TIm' dividend is lS(i4, the .jiioticn), (Ki, and tl
n'niaiiKlrr 1l> 1,..xs than tlu- divisor. Wlmt, is tl
divisor?
(i. How many acn-s in a n-('tan.u:nlar ti.-ld \ mi. Ion
and .' mi. hi-oad?
7. A hid<l<-r 7S ft. lono; .stamls iHTpcndicnlarlv a^^aim
a buildin- JIow far must, it 1,,. pulh-d „„|, aL'tii.? foe
that tln' to[» may lie lowered (i ft. y
8. A man h)an<'(l two eiiual amonnts of moiiev, one a
4% and tin; other at 4^ /, reeeivinj,' $8.50 interest pe
month. How mueh did he loan?
9. A man gave his son •• of his estate and divided th
ivst e(inally between liis wife and dan^diter, eaeh r
cciving $o()0 h'SH than half as miudi as the son. Whi
was the value of the estate ?
10. Multiply 12G|5 ]}y :{(U without rednemg to imprope:
fractions.
III
IC
I'lJAcrirvr. I'liouLOis in Aijitmmkik . oT
II Ml! S4
I was tilt'
ft. lii;;!,.
•iiislics A
«»i" cxti-a
' jraiu is
tlif wmII
t't'|», tin-
)<n'e tlu'
1111(1 tlic
is tin-
111. lu||i>-
)i<;aiiist
ill! foot
, <»ii<' af
•est {MT
(led the
at'h rc-
What
ijn'opcr
I. If ,-; of tlii'Valil.* of 11 li,M-s<f is n|iial fo ' of tin-
valurof til.' I.ani..ss, an. I I.-.tli t..,Lr,.||„.,- an- \v..ftli .>fi;Mu,
wliiit i.s Ihr valii.' of ca.'ii
2. A iiaiv is 70 Laps Im-Ioiv u Immih.I, an. I tak.-s .'» l..a|»s
wliil.. 111.. Ihmiii.1 tak.-s :i: i„ii ;{ „f t!i.- Ii..iii,.|-s l.-a|.s
.•.|iml 7 of th.- |,.n-,.-> |l<,\v nmny l.-aps will th.- IioiuhI
t t.ik(! to 011(^11 the Imiv 1
\ :{. A v..mmissioii m.-r.-lmiit sol.l laoo 1.1.1. ,,r rl.mr at
•f».7.» i».-r l»an-.-l, i-.-.-.-ivinu- ji (!oiniiii,ssi<.ii ..f :i\ \ ;,inl
iuv.-sf.-,l tifi- pro. ,1s in .-otf.-.- at 1»S,.. a poun.l,' liist
••'■•I'l.-tinir 2 ;^ (■ommissi.,n. What was his (,,iti.v .-..lu-
imssi.Mi ? How nmny p.)iin.ls ..f .-ntf.-.- ,li,l he buv .'
4. Find tin- date of niafnnfy of a not.- whi.-h falls (hw
!M» .ly. lu-foiv Mardi ir.th, 1!)(»l»; „f „„.- that falls dn,-
!»<) ily. uftei- March l.lth. 1!)((l>.
•"). What niiinl»(-r diminished l.v '.l'.\.\ ..t" its IH) 7
l.-uves 24 ? ' • • /.
n. If a man .-vny ."> m... s|m-ii.1s what li.- .-anis in 2 mo.,
and em-ns $:,;{() .-v.ry 2A m.,., how miieh ,l...-s I,,- sav., in
a year ?
7. I I»ny hai-.lware, r.-c.-ivinj; :{() 7. 2(), , 10 ,.,,1 -,7
off. and settle- tin- hill with $!>:)7.(iO. What was Hi,- Jist
price <.f the liill?
H. Divid.j if!l20() iumm- J, /.', f\ and A s.. ,|,at the
dilfen-nee h.-tw.-.-n tli.' ain.mnts n-.-.-iv.-d l.y any two
.•onse.nitive per.suns will Ix- .$-20.
9. Redne.. ^ to a decimal fraction, mnUiply the resnlt
hy 24-thou.sandths, snhtract 4 ten-thonsandths from the
product, and divide th.( remainder l)y 5-millioutlis.
O.S 1*j:a«ti( Ai. I'ltoni.EM.s in AiaTiLMETic.
1. Simplify
{^:
L' +
1
3
.)-
L
1 1 V
{^■^^-^'-i«j
J I
.075 ""
■>n .1.' +
1*. How iiiiK-Ii iimst ji watcli l.c murkoa tliat c(»st $1
so that 4 / may W dt'dtictcd and a protit of 20%
made '/
■I A n<)t(^ of $150, dated Marcli ;]()tli, 189??, was ps
•Inly 4th, ISU;}, with iutorest at (> %. Wliat was t
aiiiount ? ^V*!lat would have l>wii the amount at 7,1 %
4. Au ajiviit remitted $2S2!).0:> for tlie sale of ^'<)o<
after deducting,' $2SG.3.'3 for frei<,dit ehar<,'es and 1
e(»mmission of ,") /, What amount was received by t
ay:ent '/
"). If a tank G ft. h)ui.', 3 ft. wide, and 2 ft. dei
(•ontains 4\ Idid. of water, how deep must a tank be th
is S ft. h)n<,^ and o^ ft. wide to contain 22:| lihd. of wate
0. r> sells \ of his cattle to .1, g- to ''', ^ of the r
mainder to />, and finds that 48 head is /V of what 1
has left. I low 7nany cattle had he at first?
7. A mail purchased a liorse, jLjfivMnj? in payment h
ii(»te at () /'. At tlie end of 3 yr. G mo. he found tin
he owed .$42 interest. IIow much did the horse coi
liim ?
8. At what per cent, below par must 4| % stock I
quoted to yield the same ])er cent. <ni the investment a
'ri % f^tock at a premium of 2:;^. /, l)rokerage J % in eac
case ?
It.
)
I -^-^
M)St $120,
20 % be
was piiid
was thf
t 7i % ?
)t ^oods,
and his
d by the
ft. deep
L be that
'f water?
f the re-
what he
iieiit liis
iiid that
rse cost
took be
rneut as
in each
rKACTlCAL TlIOULKMy l.N Aj.'ITIlM Kn, :,;)
1. Fifteen jxTsons ajrreo to i)nrelhnso a t.-.H't of Innd
but three of tli.* company wirhdrawitii;, fh.- invrstment
of each IS increased .$ir,0. What does the land cost ?
2. .1 can Avalk ronnd a racecourse in 12 min /? in 1 ";
^ min, au,l C in 18 min. If they start together an.l keep
I walking, each at his own rate, l„,\v im;uiv niinntes will
I elapse before they are all three toffcther at tlit; st.ntin-
J point, and liow many times will e;,Hi have made the
' circuit f
3 n. A and Ti are partners. ^1 s ciipitnl is to /i's ;,s 5 t(»
; ^; at the end of 4 .no. A Nvitlulraws | ,.f his cnpif.l ;,n,l
; /.jTof his; ut the end of tl.e yenr their whole g-.un is
J HOO. How much of the j^^aill does each gr\ !
4. A store ma:infactnrer purchased old iron -it if"''
per 100 lb., and mak. - out of it sf<,ves wei-hi,,... I'o- ','i;'
<'.-.<;h, wliich lie sells at .$1.",^ ea.-h. How mneirdoes he
I j,'am on each 100 ll». of i,-(,n ?
n. Two raft.Ts, ea.-h 24 ft. Ion- meet at the rid-ro of ,,
voof 12 ft. above the body of the honse. How wide is
the lumsef
^ n 1 honjrhta ? interest in a const in- vessel, mihI sold
I H ot his interest t.> Ji, who afferwnrds sold 7 of i,is
' .nterest to C for .^2116. Find th,' valne of (he vessel at
tiie rate paid by C.
7 Tlie trustees of a certain school distrj.-t wish to
'mild a schoolhoiise to cost .$:,()(). The cost of coJl,.,.tiM.-
this snm,to-ether with several incidental expenses wiU
amonnt to $lS.7r,. The total cost nu.st Ik- n.ised bv -
|MX on property valued at $2(;;;()4. How much will I
I have to pay on a piece of property valiu-d at ^22r>01
CO
rUA(;TRAL Pi:()|{LE>:.S l\ ARITHMETIC.
1. T.'as at 59o., Goo., a.id 7Ge. per pound respective
are mixed in eciual quantities and sold at 81 a poui
Find tlie gain per cent.
2. Three men l)()Uf,'lit a fnetorv. A gave ^'^OOOO
gave § m<.re than A, and gave 2o % less than the to
iuuount paid by both the others. If a G % dividcMid
declared ou the capital stock, how much mouey should
receive ?
^ 3. A pole GO ft. higli broke into two pieces, such th
I of on.. i.i.M.e e<,ualled = of the other. What was tl
Icngtli of each, piece ?
4. How many cubic feet in a wall 2 ft. thick and G J
high, built about a recrtangular celhir whosc^ interi.
dimensions, when ihe wall is completed, shall be 20 1
long and IG ft. wide?
5. For how much must I make the fa.;e of a note, date
.Tnly ISth, V.m, for .'} nio., in ord.'r to get ft-om the banl
which discounts at G %, 8GG()0 ?
G. June 12th, 1902, John Smith buys of Prowse Bros
Charlottetowu, 3 yd. silk at 81.45 ; 2^ yd. lining at 20c.
3 pr. kid gloves at $1.25; 30 buttons at 25c. a dozen
i doz. handkerchiefs at 25c. ea<rn; I hat for 82.75. (,
discount of 5% is allowed on the amount of tho purchase.
Make out an itemized bill and receipt it in full.
7. If S ])ersons eat 840 worth of bread in G mo., whei
flour is 87 a barrel aud labor 840 a month, how' main
dollars' worth will 24 persons eat in 8?- mo., when flour h
8o a barrel and Inlior 850 a month ?
8._ The owner of A of a mine sold ,», of his share fo,
84().)00. At the same rate what should he who owns i? oJ
the same mine get for ^ of his share ?
^imm^^f^mm
IC.
PlUC'TlCAL I'lfODLEMS IV Ah'ITIIMETiC.
01
[)ectively,
a pound.
2()0()(), n
tlu' totill
itlfMid be
should C
w\i that
was tlic
ud G ft.
interior
•e 20 ft.
to, dated
10 bnnk,
e Bros.,
at 20c. }
dozen ;
75. (A
reliase.)
., when
r ninny
flour is
are for
lis I of
1. A farmer luis a n-i.e. ftehl in the f„rm of a nVht-
angh'd triangU'. Oik; of tlio ix-rpendiiMilar sides is"'4->
yd. long. How h)ng is the other?
_ 2. A man reeeived S.'W.^O interest on a sum h.anod
o yr. previ(»us at 7 %. What was tlie sum h,,,ne.i ?
:}. If a dealer uses 14 oz. to the iM.und, huu- nuM-h d.ws
a person actually get who ])uys 1 20 su.Ui pounds ? ll„w
nnieh per eent. does the dealer gain ?
4. If 87000, H % stock, he sohl for 8ir.0, and procet.ls
1.0 invested iu 6 % stock at 105, find tli.. dim.rem'e in the
:neome.
5. A man bought liats for 81.25 each. He sold h.-.lf of
them at a profit of '^'^ %. The remainder he s<.ld at a
loss of .8.50, and tli.Mi found that ho had ^r.M.uMl 8.^ 7 ou
the whole transaction. How nuiny hats "did he hiivV
G. .I's rate of working is to /?'s as 4 to 8, and ik is to
rs as 2 to 1. How long will it take C to d,» what I
would do in G days?
7. A bath can bo filled by the cold water pipe in 9 min
and by the hot water pipe in llf min. A p.-rsou h-avs
the bath-room aft.'r turning on both pipes simultaneonslv
and returns at the moni.mt wh.'u the bath should W
hlled. Finding, however, that the waste-pipe has b.vn
open h.> now closes it. In ;j? min. more the ))ath is full.
Ill what time would the waste-pipe empty it?
8. An estate is divid.'d among 3 i)ersoTis A, B and r
so that A has ^ of the whol.s and li twic-e as nni.'h as r
It 1 found that li has 27 ae. more than C. How lar.^e is
the estate? °
9. I t.H.k a risk at \\ ^'. re-insured ?- ot it at 2r,and \
<.f It at 2h %. What rate of iusuranc*^ do 1 g.-t on wliat
IS left ?
^J:^ J'K'.vcrn al I'ijoklkms jv Akitiimktk .
1. An Kn^Wish I,ni„.rial jrallo,, is ,t moasnro which wi
h«.M 10 Jl, avou-. of i,n.v wut,.r. A clue f.M.fc «f ,,„,
«-.-.t^T wnj^hs <J<)7.1.'}7 oz. avoir. TI.o Vvnu-h lihv is
ou1».c d<-e.nu.trr, that is, ,, cu1m> <>n u sich> of 'Mnj i,
FmmI to two phices of ch.(.inmls how many litres there ar
111 ji <>aIloii.
2. Sunplify 1 -; . <,f ! ,v, „f £:} :: ^^. „f ^.^ ,,^ j,^j _^
or 4, J l;s. j
n. A fl«,or is 27.:; U. loMif and 2(U.-i ft. wide. Wha
will Letliceostof coverin- it with matting 2. i ft wid(
at GOe. a yard ?
4. The ext.Tual dimensions of a hox (witii a lid) are as
follows: L,nj,tii 2 ft., widtii IJ ff., J,,i^.l,t, l ft. no^^
.nrniy cuh.e inehes of M.r are there in it, if the walls <,t
tiio box are li in. tliiek ?
n. Simi>lifv:
/ ^r - r «»»^»lo=> + 2:,", -j I'x (.0018:;)=^
" V ■":;
/(.ts) X (.0(160 i)
^ (.Oi;i)x(.ol5)
- 1 1
"< 1
2.i
0. A lalmrer eontra<'ts to work SO dy. for 7r,e. a dav and
to forfeit oOe. for everyday he was idle durim, that: time,
lie received .^2.1. How many days did he work ?
7 IIow mneh e<.rn at 42e„ CO.., n7c., and 7,Sc. n.-r
.nshel must hr mixed t...,ether, that the cmipomul mav
ho worth ()4c. per hiishel?
8 What is the eiy:ht root of 722204 i;{(i;50.S7;JG?
■^ms's^^'m-
PUACTICAI. PkuBLEMS IX Akithme']
TIC.
o;;
lich will
of pure
ivo. is a
.i):}7 ill.
lere are
MISCEI.I,ANEOUS.
1. A man ^ot his lu.te f„r ^]'2iH) at 90 ,lv. disronuWd
•••^ <> /., JUicl ItMit tlio proceeds for a y,.ar at 7 Mv
.vn..w.n.,. .very !)() dy., payinj. dis,.<>„„t, h. kept Ids not;
'M tl.. bank (ho wlH.le year. JIow nuu-h was ^-aine.! in
the year by tins <)i)ei-ation ?
± What amonnt nmst be invested in :{ ^' stoek whieli
sells at 92^, to fonnd a s<.holarship of .$L'()(i a year?
r'!'-?" *^'i:;i ^'''"'^^i"" *>f tin. prop,.rty in a sehool
.hstru-t 18 $800000, and the amount to ]>e raised bv
Mssessment f(,r school purposes is $!>()]. What is th'e
mte m the dollar and what will John Snnth have to pav
>f his property in the district is valued at $L>7r)0 ?
4. .1 and /^ are partners in business, vl's stock is to
/.s «s 7 IS to 11. After ;} mo. .1 withdraws ^ of Ids
t^X TV'^r' ^"^- ""^^' '^'"^" t'-" y-"-'^ ^'Hins uf
$4062 be divuled ? ^ t, i
;■). Simplify (.477 x .2;j) ^ .001219.
Standard gold contains 12 parts of pure gold to 1
fart .>f <.opper, and 20 11,. troy r.re coined into 9:J4.i
sovereigns. Find the weight of pure gold in a sovereign'
7. Sold wheat at $1 per bushel and gained $.'50 on
he quantity sold; had I sold it at $1.12A I would
did 1 SIT" ^'' "^ ^^""^^'^' ""'''■ ""^^ --^- '--^-' '
J. How many men must be ..mploy-d to uiow lOO ae
>- i-o. in 1^ dy., if 21 men can mow 72 ac. in r, dy. ?
crown.
04 PiucTicAL Problems jx Arithmetic.
1. The true discount on $572 for one year is $22.
What is tlie rate of interest?
2. If I transfer $3294 of 3i % stock to the 3 per cents,
sellftig the former at 9S,^ and jjun-hasing- the latter at
91^, what do I gain or h)se by the transaction ?
li. Three workman, A, B, C, did a certain work, and
were paid daily wages according to their skill, ^'s
eflRciency was to li's as 4 to 3 j ^'s to C's as G to 5. A
worked f) dy., B 6 dy., and G 8 dy., and the whole
amount paid for the W(n-k was $3G.25. Find what each
man receives daily.
4. Find th(; value of
5(fiH 2i) of £1 + ?i^| i'f I >f U of a ,
Express the answer in Canadian currency.
5. If the People's Bank stock sells at 147 and pays a
yearly dividend of 7 %, and the Merchants' Bank stock
sells at I.IO and pays a yearly dividend of 8 %, what will
be the difference l)etween the annual incomes whieli A
will receive if he invests Sr)()()() in the stock of each
bank ?
G. Find the value of
£1.1.'> + 2.(>(;2.') g uineas + .00781 2r) of 32s.
7. What stim must be put out at 5 %, compound
interest, to amount to $2()()() in 4 \'r. ?
8. Explain the difference lu'twci'ii true and l)ank dis-
count.
9. Simplifvf^^Ji^^^l-^^).. 2142857.
.■M^
'i^nsrwimw^'^-w^'-
Pn.vcTicAL Pnour.KMs i\ Aritiimf/i
TW.
1. I oxohaiiye an estato, wliose valtu. is £2r)4:]4 KJs Sd
stjT., for st..c.k whose pivsmt valuo is $7Gl'()().H "and
the foUowiiif; shares in s' "
is £SL'.'{4 iSs. 4(1. s)j
vahie is $9!)J)0. II*
hips : I of one whoso wliolo valne
find if of another whose wliolo
<»\v nineh wonld I h.so or piiu hy the
t.ansaetion ? Express the answer in dollars and ee.'its.
2. A ean do a j.it of ^ork in 2.-> dv.. 7? can d
-0 dy., and C in 24 dv. Tl
o it in
<ly., and then A and B 1
le tliree work toj,'ether for
after 8} dy. is rejoined hv A, who I
cave; bnt C continn*
s, and
Iiiin, and these throi^ finish tl
•nnirs J) alonsr with
u« remainder of the work
m
■. <U . more. I„ what tinio wonld I) alone have done the
uliole work ?
^} Multiply the prodnet of ..i28o7i and .0875 l,v
■••<14Ls, and divide the resnlt by .()()42,j.
4^ If GO yd. <.f carpet, 2 ft. G in. wide, be bought at
'is. 4d. ayard, to cover a room 21 ft. 9 in. loi..raii,l 14 ft
-^ m. wld.^ and tlie remnant be sold for 2s. 6d. a var<l'
how mneh will it cost to carpet the room ? ' '
5. I spent .04 + .$40 of my income, and fonnd that ,'„
of the remainder was $Hl Find my income.
G. Simplifv:
(^=
)3r
10.
of 9"^)) + Gi 4-
1
1_1_
1 - 6-A
— X
3G288
1094o5:
1
"■ l'
H
H Mi
7. I sent ten thousand and ninety-six dollars to a
Wmnipeg <.ommission merchant to purchase flour. How
many barrels could he buy at 4c. a pound, after dediu-t-
mg his commission at 2 % ?
<-^':S'
66 l*i{A(Ti( \L Problems ix Ahithmetic.
1. A person has $1000 in the 3 J per cents. How
niucli must lie also have in the 3 p*- cents that his
whole iiieonie may he $200, and what sum would he
realize hy selling out at H.'Jjj and 77^ respectively ?
'2. U 10 s<i. chains make an acre, what is the length of
a link in inches?
3. If f) men reap a field in 3J dy., working 12 hr. per
day, how long wouhl 6 boys and 9 girls take to renp n
field double the size, working 10 hr. i)er diiy, each man
doing in 1 hr. twice as much as a boy and three times as
much as a girl?
4. Which is the heavier— a pound of gold or a pound
of feathers, and an ounce of gold or an ounce of
feathei-s ? By how much in each case ?
5. Simplify :
1 +
r> + :
3+^
X f .000729
i +
2
3 + i
6i+ig-4i-n
■ ^"Y
>/.(M)62()01
6. Find the cube root of 7| to three places of decimals.
7. The .specific gravitv of atmo.spheric air, compared
with water, is .0012 ; thfc specific gravity of common gas.
compared with air, is .45. Find the specific gi-avity of
common gas compared with water.
H. An army of 215296 men is drawn up in lie form of
a solici square. How many men are there on each side?
9. A detachment of soldiers are drawn up two deep, so
as to form a hollow square. How many men are there if
the face of one side of the s(iuare shows 10 men?
PjtACTlCAL rK01iLE31>» 1\ AurniMETIt . 67
1. Siinplify
.niilft X .->,M ?:?■• " -^^
•>■-• ••■ . 1 ,( 1
'75 • •* ;i 5
li
- X .2:; it
1.1 o8.
^h of I -• ^>:i»»'«'^« ill Aml.io notation CXIV, mid in I
notation ]l!)S;j
utniiin
ir. per
Vl\\\ il
1 nuin
les as
)onn<l
ce of
n. Wliat is tli(? least common multiplo of 7, l.'», iM 2S
••{7, KM), and 12.')!
, ■•',-!, -,0,
mals.
)art'<l
jras.
ty of
m of
Me?
p, so
;re if
4. Find tli(! ciibu root of {a) 1242.'.'' (h) ""' ^.^
5. Find tlio area of a dcoajron, cadi i.f wliose sides is
25 rd.
6. If tho snn hr lOOOOOO tiiiu's as lar^'c as flic .'artli,
and the earth H()(M) miles in diameter, what is the
diameter of tlie snn ?
7. Find the vahie of
.>! J + H +^ + i + I;
8. Compose a i>ro1>k'm of wliich the sohition nniyl)e as
tMllows: £m - £.-,() Ss. = £12 12s. jrain j.er hogshead.
Then £.-,0 8s. : £12 12s. :; 100 : £2.",, jrain p^r cent.
0. What is theeost of 3 hn. 1 i)k. ."> qt. of l.erries at
1 ov. a quart ?
10. How much will an anetioneer r<'oeive for sellinjr a
piano for $4,")0, and furniture for ^'.WA), at (>J % com-
mission ?
11. Find tlie sum of 6 and 428 thousandths, 23 and 73
hundredths, 18 and 4oG thousaudth.s, and 15 and J)07
thousandths.
C8
Practical TifoiiLKMs in Akitiimetic.
1. Two nion, A ami //, liin, a paKture for $01 0'). A
I)ut8 in 4.^0 8l„.(.p f„r 7 wk, un.l /; ;»;:, Hhcr,, f,.r S U
Wliat should t'ucli pay ?
2. A del)t of ^r.'.i.r)-, ,vns dur .Afnv 2U\, 1MS(» l.ut was
settled N<.v..nil.tr 9th, 1874, at a discount of y. How
much money was paid f
3. Find the value of
(If-i.;)x.()L'.-,
y.oi
HxSxi'-x ,', X J^.
4. Find th., face of a si^dit draft costing,' $50.40 wlicn
cxchauj-e is 2J % premium.
T). Fiiul tlu! side of a square fi.'ld equal in area to a
reetanyuhir field G7() yd. lonjj l)y 2:)a yd. wide.
0. I rented a Louse for 7 % of its value, and in ,no
IH dy. I received $122.08 lent. Find the vahu, of (he
house.
7. Write out a prol.leni of whi.-li the solution is as
follows :
100 % - 20 % = 80 % left. SO - X 140 / = ll-> 7
112%-lOO%=12/i.ain. ' ^"
8. A hoy sold f bu. 5 pk. -} qt. if j.t. of herries at ."ie h
pint, and with the proceeds bought sugar at .{ 'e. a p.)und
How much sugar did he get 1
9. Tliree men enter into partnership. A puts in $4000
for 8 mo., B $0000 for 7 mo., and G $3500 for 1 vr
They gain $2320. Divide the gains.
10. A person owning 10 shares of 3 % stock sells it at
$/4 per share. With part of the proceeds he buys
enough 5 % stock at 105 to yield tlie same income. H(iw
much money had he remaining ?
Pr.\ctical Phohlem.s ix Auitiimetic.
69
1. A
l-OOMl is 10 ft. lonjr, 14 ft. wi,l,., n.Ml 10 ft. l.ijrl,
it 1ms ;j wirulow.s (j ft. l,y ;j ft. ;{ ii, , l» ,1
Hiid tli») bast'luxinl is f)
loorsT ft. l.v.'{ ft.
t«'riuf< tho room jit !.')«. |
ui. \vi(l.'. Find t
)»'i' sijium^ V!ir<l.
Iio cost of plus-
2. UiHluce a wk. 4 <]y, 20 In-. (; nu.. to tl... .Ir.-nnal of
<iO iliiys, and multiply tho ivsiilt l>v
.'}. Fiiiil the
2-/X7J,
<M>S
!» ft. wido, witli z
4. Simplify:
A + .2:i + L*
t of liniiiii: )i tank 14 ft. louj;. 7 ft. .l.'cp,
iKi ut 40(!. [u'v stpiani yanl.
. 1 L'.i
+
+ l<iH + :\ -
4- .2
)
ii +
4.1
I • -^
3
9"f^
.'). Add t(.<,'('t]iri- .'ighty-fonr million jind fift
sfvcu thoiisniid mid si.vty-cij^ht hiiiidn-d tl
i'en ; sixtv-
loiisaudtlis
hvo million and t-ii thousand s,-v<.nt,.,.n millicmtlis • tlirve
liundrcdtlKMisundlwvnty-hnn.hvdths; niut.- muli.m and
twenty-seven. Wri.e the answer in words.
f). Write" a m)te, usin.ir t^e following data • Dat.'
■'..niiary l.lth, 1!)02 ; prineipul .«{!Gr,0 ; time G mo. 4 dv •
interest 5%.
7. If grain sacfe sell at $l..TO p,.,- dozen, wliat will it
cost for the numlxT of .sa.-ks nee.'ssary to hold L' l.u.
1 pk. 4 qt. of gram, if eu(-h sack holds 2 ])u. 1 pk. ;{ qt. ?
8. Yv^i-ite out the pro])lem of whi.-h thefollowin.^ is the
solution: First, £114 8s. 4d. - 8 = £.-,72 Is. Hd."- 8 =
t:71 lOs. 2.id., yl's sh.u-o; th.Mi £114 Ss. 4d "4 -
£28 12s. Id., irs share; and £114 8s. 4d. ^8 = £14
C's share
Os. Oid.,
ro
TlLiCTlCAI. J»KO|JLK>KS JN AkiTIIAIKTIC.
tMMM 74.028.!; (r) divi.lu 27.(ir)i l.v llMl.
2. ('0 Fiii.l H.,,i„n» root (»f ]()i»();{()4();i()L>()i ; (h) fi,„i
ciihKi root of 410G.](i2.>. ^
'{. Siuiplity:
4r)()|--3.;
(H «»f .? - i «'^' ;o : (14J X ;/,)
Hiid rrduco tlio unsw.T to fiv,. pl.-u-rs of (Ic-inials.
4. Find tho compound infcnst oii £:>()() for .T yv ut 4 "^
5. lutho sr„t,Mi(.e, "Of all tho suvv.s that ev,r I saw
saw, I ,„.v.-r saw a saw saw us my saw saws," what ...r
contage of th. lett.rs are c.ousona..ts, wliat iu..rnuJ. of
he w..nls are nouns, and hy Low nni.-li p.-r ..nt. do th.
->alnundx.r,,f tho lottors fn tho voH.s exocvd the total
nnniber of tho lottors in tho ni.uns 1
0. Ilowdoosa s.i;uire diffor from a cuho? A solM-ro
romaouolof An an^lo from a trian,.iof A pv.anud
from a eouo ? A cyiindor from a prism ?
7. Tlie markot price of an article is $2.r)(). Tlio mor
of 3^ y ""^1 t"r:"f ''\ -'' -' ""'^ «*^^^ "^'"-^ '^ l'-"t
"t J.ii %. Wliat did tlie doalor pay for tho artido ?
8. A merchant l.ou-ht 4(iO bhl. of flour at $:] 75 p,.,
barnl Ho s.nt tho flour to an aj^ont, wiio sold it at an
advance of ^ % and char^.o,! J /^ commission. The nnr-
/
cluint tlicn sent the not proco.-ds to an agont to purchaso
niolassos, after d<"ductin{r a conimissiou of 1 j -/ ij^w
many galh)ns, at GOc, could tho niront puroliasoT
9. If 200 men in 12 dy. of 8 h.-. <....oh can dig a trench
100 yd. long, 18 ft. wid.> ..nd 4 ^=1. ;\^..,
days of 10 lir. each will 90 ju<
4 yd. wide, and 3 yd. deep ?
1>, i;i liow man
11 <lig a treucli l.J5() ft. loug
y
^^i^^Tli^r^S^TTTr^
J*ltACTI(AL I'ljnm.KMs l\ \
jariLMt'iir. 7
I
find
1. (i'wv rule oi- foiiiiiilii lor lliKliiii,' |M-n-(.|i(iiv'.- \v|i.t,
hnsi' 1111(1 nitn jnv pvt'ii ; fm- HilIiiij,^ mt.- wli.ri U.x- an.l
lUiiMiiiit an* f^ivt'ii.
2. Find the viiln.-s of ,•{.;{-.■) x l.ii x l.s ; n; ; |((.f»|(; ;
''i.37'} -■ 4.7} ■ .■{.,"> + J.s;"i 4- .(■; ^ l
of th»» result.*
.'{. Expns.s .;{7.") of a jru
in<
)llld tillll lilc |i|<m|||<-|
>t' a n-own 4 .;; of
7s. r»d. ^ U of LM. as th.' (l.( inmi of 1(1
4. Find Uw siiuaiv r.M.is ,,f .;j. l(;.:{r,;jf>;;(i^ j | j^ o-,,, .{- 1,
iind .(MJo.
.'). Divide £110
aniui;,' K 11,
•'hilcb'fii, so tli;«t each niiii!'. -I,
of 2 women, and the .{2 woin
luueh as the 4S childreti.
•"IL \Voi.ii.|i, III,,] \s
wii' «'iiial tlie ^||,|(•es
uiil r, r.-iv,. twice as
Kii- siini is .">1 and
0. Find two nnmlKTs, such tiial il
their difference 1.').
7. At the Canihridjre local exiiniiiiutions the muni
junior stn<h iils who jin'sented themselves at tli
? centres for examinati
lel- oi
res tor exannnatK.n m mathematics pive a eertaii,
average i»ercentaj,'e, and this avenij^'e is diminished l.y
2!f if Lond<m, and the !)," students which it furnished,
he omitted. How many were tliere in m11 y
S. At 1 <i'cl(.ck the minute-hand is o min. I,,!, in,] ji,,.
hoin--hand. In how many minutes will it, l.c the same
distance in front ?
\). Find the cubic root of .01, .'{;5(>7().l(il, SOfiTTr^JSKil,
and 2.5.
10. Simplify.
2 i
\ of 1 J
!__■ '^l 2.] ^ • ^ 7 ^ l(».i
i 3 + 1 1 (:;r-\i^J
X 1 '>'
72 Practical Pkoblems iv An
ITlIMETic.
1. If 1 oz. 4 (Iwt. 9 gr. est £1 lis. ()J,1., what is the
pricu of 5 oz. 17 dwt. ? j , t i.> i,u
PROPORTION.
2. If i„ 2(U(; dy. of Hi l.r. .,.,.1,, 12 ,nn. l>„i],l a wall
->(> ft lo„^ 28 ft. hi,.h, a,Mi li ft. thi.k, in how ,n,.nv
Onys of 2 h... ea,.h will 9 men build a wall 9G ft. lo„.
-'1 ft. Iiij.h, and IJft. thick? ^
■I The tax to' bo raised in a town is .SIGS?.",, and the
assessed valuation of the property is 8ir,()(MM)() wint
amount (,f tax will a man have to pav wln.se pro,>ertv is
assessed at -SGoOO ? i i '.v i^
i. A and n can plougli 22J nc. of land in 3 dv • /;
and C c.m plough 6 ae. in 1 dy., and .1 and C 13 'ac! i„
- (ly. How many acres <;. ■ ach plouj,'h per day ?
5. If A can do a piece of work bv himself in 1 hr 7?
in 3 hr., C in f, hr., and /> in 7 hr., in vvliat ti.ne can they
do thn'c times as much, all working together ?
G. If 120 men In 3 dy. of 12 hr. each, can dig a trench
'JO yd. h.ng, 2 ft. broad, and 4 ft. deep, how many men
would l,e reciunvd to dig a trench 50 yd. h.njr G fl
deep, njid U ft. broad in 9 dy. of V, hr. ?
7. A tract of land 7495 ac. 3 ro. 32 rd. is to be divided
among a regiment consisting of a colonel, a major 5
<-uptains, 9 lieuteiumts, G ensigns, 20 sergeants, and 450
privates, so that a sergeant is to have twice as nmch as a '
private, an c.isign 8 shaivs. a lic-utenant 12, a captaiix 20,
the major JO, an.l the eolom-l 50. Find tho shai-e of each
and the value of the Juud at 83 an ar-re.
> ^W^'^&^rC: Xvif :^^:, .jfW.
PitAcTR'AL Problems ix AuiTiniETif, 73
1. A alone could porforin a pii-eo of work in 12 lir. • ^l
and f ' t()j,^('ther could do it in o hr., and r"s woi-k is to
/i's us 2 is to ;J. The work must ])c coiupl.'trd l)y noon.
A bej^'ins work at o a.m. At what hour jiuist />' .-lud ('
join him so tliat tlie work may be complctfd in time?
2. If 4 men and 18 l)oys working together can do
three times as nuieh w<»rk i»er day as 2 men and 4 l.ovs
together, compare tlit« work of a boy witli that (.f a maii.
3. If battleship having 1S()() „i,.,i on ])ojird and pro-
visions enough for l.i yr., sliould lose \ of lier men, how
long would the provisions lasl the remaindi-r?
4. If 1.") men, working (i hr. 40 min. per day, can diir
a trench 48 ft. long, 8 ft. wide, and :] ft. deep in 12 dy!^
Iiow many hours a day must 2.') men w(.rk to dig a
treneli 3G ft. long, 12 ft. wide, an<l .'] ft. deep?
INTEREST AND PERCENTAGE.
"). A sum of numey amounts in 10 yi-. at 7"/ t(.
82898.r)(). Ill how many years will "it amount to
?^.■{7;]:i.yo y
G. If by selling goods f<»r .%70.S0 T h.se 14"^, l,ow
tiuich i)er cent, should 1 have lost or gained if 1 Imd sohl
them f<u- 8707.20 ?
7. What simi put out at 0%, simple interest, will
amount to 8884.50 in HI yr. ?
8. If 3^ % would b(^ gained by selling 714 qr. of wheat
for 88807.88, at what i)riee per (juarter must it ])o sold to
realize a gain of 4^ ':[ ? •
9. A savings bank pays ^ "/ on deposits that remain
<i mo., interest i)ayable semi-annually. At th(> end of
2 yr. what amount is due .-i person who has deposited
f}2o at the beginning of each iutere.st period ?
^■;si-^.':l:;^£l
74 VRAVncxL VmULEyiS I\ AKIXIlilE-J
TIC.
1. A Tiu'ivliunt bought goods aiul .sold them for P4'>()0
losing 10 %. Wluit did the goods eost liim ? ^ " '
2. Find the eompound interest on eiOOO for 2 yr. at
'H %> payable quarterly.
3. What is the amount of $600 for 168 yr. at 6 7
simple interest? ' ^°
4 A note for .^2500, dated July 1st, 1;S9S, was to be paid
October 2i,d, 1900, with eompnund interest at 6 %. Find
the amount to be i)aid O(!tober 2nd.
5. 11800. Annandale, Septemlu-r 10th, 1900
For vahu^ received, T promise to pay Patrick Ri'ee
or ord.T, Kiirhteen Hundred Dollars /'.;;, in one year'
witu interest at 6%. C. 0. Howled t.
A^ payment of .^6(H) was made „u January 25th, 1902.
What was the balance due July l,")th, 1902?
6. I ho]<l a note for 83600, the interest on which from
Its date t<, October 29th, 1890, at 7 % amounts t<.
'^14.J8.oO. Find th<' date of the note ?
7. Find the simple interest on 17000 eagles, at 6 7 f,,,-
''},'\, yr.
H. A Cardigan merclumt bought dry go.nls to the
mnountof ^Vm f„, ,;„],. ,,,. kept them f(.r ^ vr. an.i
thi'ii sold theni f„r 15 % advance on their cost, at 4 mo
<*redit. Find his profit, interest 6 7.
9. Simi)lity
FRACTIONS.
)
.'^ <'^lf)-!(^-f'6) + (:!>?lA)l
Practical Pkoulems in AuiTiiMEiic.
to
1. Express jis a decimal :
60
! .19
1 +
(
()(»
Ol
)
2. Divide the sum of 4i], 7'^, 3,^^ ^'V tlie difFereiiee
between ]J ami 8,^, and multiply the result by 7.\.
3. Simplify:
(
+ Ir. + .37;-) +
C.lM
.oor.!?:
_'.j
4. Simplify
(789 - JH!))
(.7.") - .07
) X ./.)<»
f S)
— - - .00090.
llH■^
.04 i
5. Multiply 7. ;■{(■) by 3.:297 and ••xpr.-ss th
tj answer as a
decimal fraction.
6. Simi)lify
•U + 4^ - m -;- 3?)
3 +
o +
,i42sn7
7. If the difference lu'tween 7.") and ;:' of 121? + =^ of
4S§ be t«,ken from l.lOi, by hoAv many timt-s f, of 1 ^ of 4
- 24 should the r(\sult be multiplied to ])roduee 342 ,';,'„ ?
■S. Find the value of
(1?. -*)x(i-,"o) . ^of bi
i of 4i of
) I
(2H+3i)x(H', 4.i)
2H + (3ixSi, -4i
21
+
}% ,1 ^ S •_• 1 .! T 1
+
1 i_ ••«
70 PiucTicAL Problems m Arithmetic.
1. 7f 1 of -i-(§^>fl.^) , o ,
what will ^•^'^''^•^i)- 2.5
PMS^NT WORTH AND DISCOUNT.
lM.Na 1,. ,2 „,o. l.en,.., u.mI sol.l thoTu at once for $07-, r^Q
4. A ],ill of .$;j;527.50 dmwn on Jannary Isf, 1901 at
8 nm. IS discounted by a ha„kor on the ] tb Apri io
;>--.^ at 4 %. What does the hanker .ain by Sno '
in- interest instead of true discount /
J. Find tlie present worth of a note of $:mM ,h,e
80 dy. hence at U 7.
(i. A l.ill of $SL>.-) w,is drawn on 0<.tol.pr 24tlr iqni .,.
1 111(1 the present worth of it.
<'"nnted 146 dy. before bein^ due, at T, %.
«. A merchant bouo^ht 50(» bbl. flour at $6.o() per
'-•■'-1 and sold it imn.e<liately at $7.2:, per barrel Iv
|-'v.i.g ui payment ,, note due :{ mo. henc. which he
luu discounted at a bank at G %. What did he ,.at
on the flour? ^
9. If $22 is the true discount on $572 for on,^ year
what IS the rate of interest? ' '
PR.\(TICAL PROHLKMS IN Al{ITIIMETI('.
i i
1. A bill for $6900 drawn on Jminnry Isf, was piv-
soutt'd for payiiu'iit a dy. afterwards. Find the i)r('sent
worth, money Ix'ing wortli 4 %.
2. Find the present wortli of $200 dne mu. lien.'e at
' J
.'3. A Geor«,'etown merehajit ^wm^ for 4 earcasses of
l>ork a bill of $7:} due in 1 mo., and sold tlie ]M)rk at
onee for a note of $S7 at 4 m(». Find the niereluint's
jraiu or loss per cent., interest at Ah %.
4. Show that the diflFereiu .. between the interest an<l
the true discount on the same sum is the inter.st on the
di.seount.
o. Find the amount which a banker jrains bv dis-
<'(»nntiug a bill of $24r)l.;M, drawn July 12t]i at 4 m...
and discounted September .'Jrd, at a /^ per year.
G. A person discounted a bill at the Bank of Halifax
and received $37.10 less than the fae<^ (.f the bill, if
true discount only were collected, what should li<' reeeiv.-
for his bill, intei'cst at 5 % ?
STOCKS.
7. At what price must T buy H ^.cr cent, stock so that
nfter payinj,' an income tax of (>?, 1 may hav<' a, net in-
eonie of 4 % on mv outlay?
S. I invest $2n") f(.r 8 yr. at 7 % and tln-n buy bank
st(.ck, 12 per cents, at n4.i. ITow mueh stock (hi I get ?
9. The income (»f a railway company would jiay 4 ^'
dividend were there no preferejice shares; but $200000
of the stock being of sueli shares and guaranteed f) %,
the ordinary shareholders receive only ?>h %. What is
the whole amount of stock?
/8
P«A(TI( AL PaoiiLKMS IN' AhITILMETIC.
^ H^ < ars at 90 H.Hl n.vesf .nj, in 4 p.v c.nLs at llo
ttiu.^ ar. j«. After rcceiVMM' a Ji-ilf v,.....'. ,t • i ^ "
^U,K What was tl.o original sum inv.stod ? ^
.^ 1 invest .r)40 in fi jht ocnt. stock at O-i .
*<inji 1 ''/ Tr 1 .">i«>(K ac :^)i, conunis-
•^1011 i ^^. Ilou' much stock do I receive ?
4. mat sum Tuust be invested iu 4 per cent slock at
on m order tliat after paving an inco/ne tax of 4 ,,
th.' doHar, I may liave au inc mie of $400 ?
proceeds ,n 4 per cent, stock at 76 ana the rel' .^ n
^^1- cents at 114. mat is the alterati<.n in 1 -/i;;;
o a 89I'" ^^'^'VT-"""' ' •^•"-•'« •^■•vidend he sells
out at 89,. The whole increase <ui his capital is $r>o
Wliat did he invest? ' '-^ -Ti —
7 A person holdin.s,^ ,£l.-iOO st.Tlinjr stock in 3 i>er
»"•). tuul the g-ain in uifojue if £1 ^ $4^7.
S. I invest .$10000 in the T, per cuts .,t 0". ir
much nnist I also invest in tlu. r "^'"/'^ ^•*- ""«•
X .u.so in\(st m tlie G per cents at V^O tint
myinc<miemay l.e$17.-,0? '-"'lu-it
n A invests i of his fortune in fhe 5 per cents at «m
^1 ivcou-os therefron. an annual divh^ul of ^ioon
He invests tl.o ren.ainder of i,is fortune h. the 6 p^-r .
«<'uts, and denves tlu'n,.e an in.-om.. of $3800 \f Xt
^'•'-^v.s the latter stu.kpurci,ns..d:^ "'
()()()() in
at 115.
I Oi JH'l-
(1 Upon
pifiil is
•iiunis-
• M'k at
4('. on
stoek
r»f flic
Icr in
lis in-
ij per
sells
$122. ■
ts, at .;
How -:
thaf .-.
it !m
90(1.
!>•■'•
vllJit
riiALTICAI. I'liOliJ.KMS IN A IMTHM KTI( . 7!)
I
I MENSURATION.
1. What is tlic /JifT'.'n-ncc hctw.-.'n S s,,. ff nnd Hft
square? The dittVirn.-e m a.va l.eiween 1 s.,. ft. and"
J 1 ft. s<pnu'e ?
J 2. Three eireles. eaeh 40 nl. in diameter, foueh eaeh
I <.ther externally. What is the area <,r the spaee .-nelosed
I hetweeii the eireles ^
• .1 Find the cost of pavin- a re.-tan-nlar eourtvard
' whose len^rth is (j:} f'. an.l wulth 4-. It., it l.ein.^ pave.l
with pehldes at Is. Od. pev .sqnare yard, ex^vpt a. foot-
path whieh runs the whole In.-th, .", ft. ;{ in. l.road, and
wh.eh ,s pave,l with tia-stones at .{s. per s.p.are vard.
1 lie bill to be ])aid in Canadian eurreney.
4. Find the cost of hrvin- a diteh dn'ir round a jr-mlen
^■M yd. lonj,' and 72; yd. wide, th.' dit.-h bein.^ 4 ft
'i'M-p and 2S ft. uide, and <-osting 2e. per cubic foot"!
^>. Thirty-two yards of carpet. 2^ ft. wide, an. used in
niakui-a s,|uare rii- winch is laid evenly in the centre
"1 a reetaniiidar room 24 ff. }>-, Is.i ft. Find the dis-
iMuee the carpet is fn.ni the suh-s of the room, and what
IS the area of the uneovfred portion of th<. floor?
f). A room is 21 ff. huiir. 1') ti. (I in. wide. 10 ft hbrh •
It contains ;{ windows, th- re.-ess.-s of which reai-h" t/»
'Ik- c'duio., and are 4 ft. G in. wide; there are in it 4
doors, (>aeh (5 ft. (i in. hij^h and ;5 ft. :i m. ^^■\do, ■ the fire
place IS (5 ft, wi.io .,na ^ ^^ ,,i^,j^ . ,^ ^j,;,.,;,,,, , f, ^ .^^
deep nnis ronnd the wall... Find the cost of paperin.^
Hie room at .jc. p.r .Mjuaiv fooi.
' Find thr ar<-a of a s.inar.' wli<..se side is 17.02.1 ch.
^. Wliat i.s thf a?'ea of .;i triani'!!- vc'.in-fu- \;^^i. ;. - o -■
•h. and altitude 0.4 eh. :
80
PltAr'TTfAL PriOIlLKMS IN AlUTIIMKTIC.
1. II<nv mnuy acr.s are thoro i„ a trim,^.ular fldc
wli„so tl»r<'e sides are 49, r,()J, and 2r,;;», d.. ?
2. If the],aso<,f a rijrl.t.anjrl,.d tnan^.lo is 58 and tlu
periK.ndHM.lar '.io ft., ilnd the l.ypnthenu;..
KHi ^'"^ !'!*; "'"'' ''^ '' trapezium wl.ose diafrenal i.
H'Ht tt. and tJie perpendioulars -.0^ ft. and 00^ ft.
4. Tli.. jmrallel sidrs of a trapezoid are 12.41 and 8 '>'>
c'u., also the perpen.lieuhir is 5.1:. eh. Find the area. ""
r>. Find tl,e,an.a <.f a hexag.ni whoso side is 14.G ft
and pei"pen<h(MiIar 12.04 ft.
G. Find the area of tlie figm-e .1 Ji
CJ)EF, snpp<»sing the folh.wing
dnnensii.na are given: .1 r,\)\- Ji ii
10; andiv'^>,4. ' ' '''
7. The length of an irregnlar figure is 50 vd. and its
hivadths at seven e,,ui,lisfunt phiees are 5.5,*G.2, 7 3 G
7.0, 7, and 8.G. What is its area? ' ' '
8. The diameter of a eirele is 34 ft. Wlutt is tlie
length ot the cireumferenee?
9. Find tlie radius of a eirele wliose are. is 1 ro.
^V\ Find the area of a ein-le wh<,se einMunferenee is
11. The differenee between the diameters of two e.m-
centne e.reles is 5, the greater diam.f.r b,.i„g i.-,. Find
tiie area (.f the ring formed by the cireles.
12. How many imperial gallons will a tank in the
torn, ot a eube eontaiii if one side of the eube is 7.5 ft. ?
wJ* 7'"\V"'"/^'" ""^'^^ <*'>»<<'n^sof ablo<.kof granite
whose length .s 10 ft., Us width 5^ n., and depth ^J ft. ?
I'KA< IK AJ. PUOULKJIS I\ AkITMMETIC.
81
1. Find tlie si.li.lity of a oylindcr wl
15 ft. and (tircuinfeiviKMi of its Jmse 2() ft.
lose height is
4.G ft.
<
I
11(1 its II
7.3, G,
s tlio
"^e IS J
' con-
Fiud
I the
ft. ?
initc
ft.?
2. Find the solidity of u <'oii(', tlui diiuin'ter of whose
base is 18 iu. and its altitude l.j ft.
:;. Fiud the convex surface of a sphere who.s<. diameter
is 18 in.
4. Find the .^olid eontents of
is 18 ft.
'i. What are tli
a sphere whose radiu^
e eontents ()f t\v(» niahofrany plank.s,
•'ueh 12.^ ft. lonj; hy 11 in. wide?
f). Tlie lenjrth of a pieee of .'uinan-d tinil.er is 49 ft.
and its ends are eiinal scpuires wliose sides are eaeh
1.04 ft. What is the solidity ?
7. The eireuniferenee of a tree in four diflFerent plaees
is as foHows: in the first ])laee, 3'^ ft.; se<-ond place,
'y^ ft.; tliird place, 4^ ft.; fourth place, 4,"., ft.; and the
length of the tree is 15 ft. What is the solidity ?
8. The weight of an iron sliot used yearly at the
Caledonian sports is IS 11,. Wliat is it.s dianuierf
Another shot weighs 12 Ih. WHiat is its diameter?
J>. The three sides of a triangle are 12, 20, and 28.
What is the area ?
10. Wishing to find the lieight of the flagimle on
Anuandale st;hool lawn I procui-ed a staff 5 ft. in length,
and i>laeing it in the sunshine, perpendicular to the
horizon, I foun<l its shadow to be 4.1 ft. Then I
measured the .sjiwdow of the flagpole, which I f,mnd to
be4:{.4G ft. What was the length of the flagi>ole ?
11. A tract of land in the form of an obtuse-angled
triangle contains 1 ac. ; two of the sides are 20 an<l
40 po. long. Fiud the third side.
82
PUA. TICAI. JY-onr.KMS IN AlMTHMKT,,,
1. If tho Jin.ar Hi.l. of u ..,.,t,ii„ <.„1.. 1,. increases]
1 u, «urfH..o <jf tlu. <.uho will be i„e.va..d 2^ "u
Hud till) Kido ,|f t|,„ ,,,|||^, '" ""!• 'u.
2- Find tlu, c„„t,.,.ts „t a t.-,.o wh„»c i,.„„tl, is 17* ft
"."1 wln,.l, gin. i„ flv,. differ,.,,, „1,„,„» ..s', i:;yjif:
, t.o first ,, la,,,, .,4:, ,;, ia tl,!, »,,,„„,, - "o um';:
thu-d, 6.1.,; ,„ u,e f„„,.,I,, 4.74. and i„ ,l„. flftl, ;l in
ii.MuiKll,»of il„. mfi.Ts a.v l(lft.und \2 ft. th„ end
o ,„ si,.,,.,,.,. ,s ,,,„,.,.,, „„ „,.. |,i ^^.^,. ^_,,| ^^ i
Fn 1 th,. I,.„,„ 1, „(. tl„, „,„.,■,,,„ ,,,,i„,, ~^-
of the roof, and the width „f the house. "
DECIMALS.
itf ,.'"•■ ■*"•■' ''^' '■■-*' <■') '""J ""■ .■< >t
tJie tlirce answers.
r, A,U1 the followin.ir ,„„ni„,, ,^i^|,„„^ .
^nu.tH.ns:-;i.Ow, 2.0G;i, 8.210, 4.5<>, mui ^i.m.
(y. Add tojrethor .5 of n ),i„f i .,k ., . __
.> of u peck and ^.pt. '^- ^ l**^' - 4t., .7. ot n,n.,
7. Simplify-:
■ S.i of . Ss. + ., •)..-. „f2.tr„iii,.H.s 4-1. ,S« ,f Ds.
5 1 AHV^ ^ ■"">
■^K 2o
l,y
8. Divide !(20() + .()2-.nx.,s{+(.,si ,.,- ^., „. -,,,
-'.07of .^x300x,f)0.:j • ^ ^ •'-n.x.f of ,•)!
PRACTtCAL PuoiiLKAIS IN AumiMKTlc. H'J
1. Simplify:
(;;47.H4-=- 10.87) X i(.<M)2r) + .or/) -^ r>0|
(lOHO X :].-27) ^ 10.90 _ (75JO-: ;{.y:,)
^ '^•' ' "hi:; '2 i \
5i -0.042 2.4 + 7.^ \ "~
-. FilHl tii(3 Villllf of
.1 -J 1 7 » •
f3. 1 2 + fAmiry .< X " »( >«;(;.-)
4.;{7.")
^80 - f .01
.( )(»()().
O 7 7
- I I I
•*{. Find iUr valiui of £.(;:{4:!7."> + .02.') of 2.'»s. +- ..'J2."i of
•iOs. - 2.1 j.i of .Is. 8-^i. (liviiK'd hy 4^
4. Find tiu' vidiu) of llUiid milrs.
"). Simplify:
( '.07.') X 0.07.')) - (0.00.1 X 0.00.'))
0.75-0.05 ^ snim.imn.
PROBI^EMS REI.ATING TO WORK.
<i. If A work.s for 9 lir. jind li for 8 hr. u d.-iy, Init Ti
'I'x's ill (.lie iK.iir i^ more work than .1, 'in l„.w
many duys of 9 hr. each will the two workinj,' to^r^lu'r
iK'cojuplish ji tusk whi(-h would take .1 uh.nu (> dy. of
■"> hr. cacJi ?
7. If yi can do a piece of work in 5 dy., /i twice a.s
Muich in 7dy., and T four times a.s much in 11 dy., in
wiuit time can ^l, 7?, and (! together do three tiniys the
amount of work ?
8. A boy hired with a farmer for Ifi weeks fo i and
a coat. At the end of 10 weeks the hoy (luit.s work and
receives §6.35 and the coat. Find the value of the coat.
- i-'r-
MICROCOPY RESOLUTION TEST CHART
(ANSI and ISO TEST CHART No. 2)
1.0
I.I
1.25
■ so
1^ 1^
2.2
13.2
?r 14.0
2.0
1.8
^ APPLIED IIVMGE Inc
Sr 1653 Eost Mam Street
r.S Roctiester, New York 14609 USA
^S (716) 482 - 0300 - Ptione
a^ (716) 288 - 5989 - Fax
84 PuACTicAL Problems i\ Ahitiimktk .
1. What will it cost to paint a room 20J: ft. louj,',
18^ ft. wide, aud 10 ft. high if there are two windovvs
eaoli 7 ft. by 4 ft., aud the work costs 62^c. per square
yard ?
2. A aud B agree to do a piece of work for $36 ; A
could do it in 9 dy. aud B in 12 dy.; but C joining them,
the work is done in 4 dy. How should the money be
divided ?
3. If 15 men dig a tren-h 48 ft. long and 2§ yd. wide
in 14f dy., in how many days would 25 men dig a trench
of the same depth, but 12 yd. long aud 12 ft wideP
4. Tom, Dick, aud Harry, working together, can do a
piece of work in 5 dy. Dick can do half as much as
Tom and Hairy together, and Harry can do J as much
as Dick and Tom together. They rec<'ive $45 for the
work. What is each person's share ?
5. Eight men were hired to do a certain work. By
five of them failing to appear the work was prolonged
44 dy. In what time could the eight men have done the
work?
6. Write out a problem of which the following is the
solution : 12 X 7^ dy. = 87 dy. work to do ; 12 x 5^ dy.
= G6 dy. work done ; 87 - 66 = 21 dy. work to do by
the 4 men; 21 - 4 = 5|; 5J - 5J = | dy. Answer.
7. If the rate of wages of a man, a womau, and a
child be as 6, 3, aud 1, and 25 men, 30 women, and 10
children get $320 for 10 dy. work, find how much 32
men, 36 women, aud 72 children should get for 8 dy.
work.
8. A, B, and C mow a field for $12. A mows as much
as B aud C less 5 ac, and 7? as much as A and G less
10 ac. If A receives $5, how much should B aud C each
receive ?
Practical Pkodlkms i.v Auitilmetic. S^!
PROFIT AND I^OSS.
1. A dealer sold a caiTiaj^e tor $7(5, and tliere])y
clcart'd ^ of his luouey ou it. If lio had sold it for $.SS
what would ho have gained jxT cent. ?
2. I bought cotton for 8^c. per yard, which was 20 %
less than the asking price, and the asking pi-iee w.-is
12| % more than the cost. What did the merchant gain
or lose ou each yard he sold to me ?
3. A schooll)oy htiys slate i)en(!ils at "x-. a 'lozen k»i<1
sells them at the rate of 3 for 2(;. "What does he irain
per cent. ?
4. By selling 10 lb. of tea for $r)A{) I gain 12^ %.
What do I gain or lose per (!ent. by selling 2.> lb. of the
same tea for $14.25?
5. A grocer mixes 68 lb. of tea at 32c. a pound with
36 11>. worth 28c. a pound. At what jjrice mu.st he sell
the mixture to gain 13 i\c. a pound ?
6. How mu'jh per cent, above cost must a man inark
his goods so that he may take off 30 % from the market
price and still make 30 % on the cost?
7. A btiys a tract of land at $42 an acre. If he sells
i- of it to B at $21 an acre, J- of the renminder to C at
$()3 an acre, | of what then remains to J) at $12.7.j for \
of an acre, and the remainder, 193 J, ac, to U at $72 for
§ of an acre, what is his gain or loss ?
8. A man bought a farm of 165 ac. 2 ro. 32 po. for a
certain sum and sold it immediately at $33.50 per acre,
and took a note for the amount, payable in 5 mo. 15 dy.
at 7 % simple interest. He got the note discounted at
once. How much money did he make on the transac-
^ tion if he bouglit the farm for $4986 ?
86
TlJACTK AL PlIOlJI.K.MS JX A KITII.MKTl,
1. Tin. 4 iHT n-i.ts an, .s.-Uin^, ,,t l;{(i :uul ll„, ;j „,.,•
n'Mts ut 102. Uovv „„,.•!. would T pti„ or ],.... in Uu.L
kv s,.!],,..- cut moi) stu,.k iufh.. fonn.-r an.l iuv.stin-
tlic procH't'ds in tli.- latici-? *
2 A irKMrluint failing, iu Lushu-ss can pav 70,.. <,u th.
dollar. JI.. cm.rs to pay ],i.s whuio iud.l.h.du.'ss iu r,
.vcars If h.s nvditcrs NviU allow l.i.a to ^.„ on witli his
•>u«iue.ss. Ills off.T iHMuj. ac-rptr,!, ],ow luuc-li will his
.•mlitors lose iu the 5 y.-ars if niou.'v is worth 7 7
simido i,,l.r,.st ami the merdmut pays no iutercst on lii^
mdt'btt'dness?
3. A luerc'hunt pur.-liascd in ]\Iontreal p.ods oostin^
*-0G0 on the foUowinj,^ terms: G nio. credit or .1 7 off
toi- cash. Ho cliose the latter nn.l kept the goo.ls for
(.0 days before sellinjr them; he sold tliem on 1 year's
credit at 20% advance. What were his profits on tlie
whole transaction ?
4. What was the cost to tlie wholesale dealer of L'oods
sold by the retailer for 140 ^ndnc.is, if the whoh-sale
<lealer makes a profit of 5 % an.l the retail dealer Kiji V ^
(Tive answer iu Canadian currency.
TAX^S AND DUTIJ^S.
5. If the rent of 18 ac. for 3 mo. be $60, what should
l)e the annual rent of a farm of '540 ac. whose average
•luality IS only half as -ood as that of the former? And
If the land tax is U % ou ^^ of the value of the land, find
the amount of taxes payable on the .-,40-ac. farm if the
rent paid is 10 ^ of the value of the land.
.,>.• w:--'*
I*i:a(ti(al I'|{oi!lkms in Aimtifmktic S7
1. A ^r.M'(T huys ]:>() 11,. rolfcc ,il llr. [k-v ixmiikI, :iimI
:'.!) 11). chicory .-it G.'. per pomid : lie p;;ys ;m import duly
ol' \2.l y,atl r, I Ion' III, una mixes uiid sells them at 2r,e,
|)cr ixmiid, hut l.y the us.- of a fals.' wcii-ht i-aius J-o/,,
.►u every pound sold. Find (he perccntaj,'e"of prolii
made on the outlay.
2. J)efiue (^0 a tax, (h) direct tax, (r) p„ll tax, (</) in-
dn-ect tax, (. ) property tax.
.'{. Find the duty payable on ,S(i .j.jdid. of currants
\veif,diinir oil an awraiiv 471 ll.s., at ;c. per [xiund, allow-
inj,' a reducttioii of S.^ / i\n- (,,,;_
4. The taxable property of a crtain school di.strict in
P. E. Ishmd is vaiu.-d at ^l!)4.-)(). If the following
amounts are voted at tlu! annual school nieetinL-- lo run
t!.e school for the current year, find the amount of school
tax payable on a farm valued at $2400, supp,osiug- thei-e
are 11 persons in the districi; who pay a poll-tax" of .$1
each: Supplement to teacher's salary, $35; eoutiugent
expenses, $28.40 ; schoolhou.se rej)airs, $98.
5. An estate iu Ireland was let for £480 a year, less a
hmdlord's tax of l.nl. in the pound. If the rent is
reduced to £4r)0 a year and the taxes rise to Kid. in th<-
pound, l)y how mu(!h per cent, will the himUord's profits
'•e reduced ?
<). The rental of a hou.se is 11 / of three-fourths its
v-iUue, and the taxes are 40 % of the rental. What is the
value of the hou.se if the taxes amount lo $46 ?
7. The exj)en.se of supporting a district school for a
year is $398.00. Of this amount $22.) is paid l)y (iovern-
mt. The rat.; of gc. on the dollar is levied to pay the
^\lmt is
IU(
lance
the assessment of the district?
3 i
88
J*I{A( riCAL I'UOHLEMS JN AlUTIIAIKTlC.
1. If the villii^^H (.f Ti«r„isli, uhi.-h hns $-)()()()(» of
taxj.hle properly, is uss.vsMOil $\].U), what is .I's tax if
his i)n.p('Hy is valut'd at $1400?
SQUARE AND CUBE ROOTS.
2. Find tlic siiiiarc i-o(»t of 4!)0()!>S<M),S4()2r)(;.
8. Find tlic sciiuuc nx.t of (i4.44r)2i()()4!)aS27 and of
.0(M>04(>9(;.
4. Siinpiifv >'™^''"i + rmummi
'). Dividi! tlio culKM-oot of H:i7Al')(HH) hy | ,'. ,,f 12,^ of
-.^ "f (I+r!- 7)<»f !;;! and diniiuish the result liy the
s<piar«! root of 1();{2()()244.
G. A..-ango in order of iiia<iiiitude:
(2.403)% . vC,r,7.19G()2.3, .03.% fJJm.
7. Tlie cubic contents of tlie interior of a box is 1296
cu. in. If tlie box is made of 1-in. boards and has a
cover, and tlie length, widtli, and depth of tlie box ure in
proportion to each other as .",, ;u, and 2, find the cost of
painting the outside of the box at 15c. per scpiare foot.
8. A cubical tank is t.. be built to hold 200 gal. of
water. What must be its depth ?
9. Give the rule for finding the cube root of a common
fractit)ii.
10. Seven-eighths of the scpiare of a number is 315|
What is the number y
11. Find the value of
S 2 Bo ,'. tin 4
t (i S « -^ 15 if
V 13 6 4 4 ^ i>Tst
G.C.I), of 945, 1560, and 22683.
I'KACTK AL I'ltOMI.KMS 1\ AlJITirM KTIC. St)
1. Prov(^ )>y nil example tliiit tlic s((uaT-o root of tlic
lirndiict of two or moiv imiiilu'r.s is niiuil to tlif prudiu-t
of tlR'ir !S(|Ujire roots.
2. Tlic square of twice a iiiunlM'r is liMi. Wliat is the
iniiiilier?
MEASUREMENTS,
■ i. A eirele and a sijiian^ eaeli li.is a eireiiit of l.'».i ft.
W'hieli lias tlie greater area ?
4. Apiece of land is .'{:;(! ft. Ion-,', and .•ontains M sij.
chains. What is its width ?
."). How many sleepers, placed 2 ft. apart, and Imw much
iron u.siui,' 2."> 11). t(> the yard ut rails, will 1»e re(iuired to
CO
nstruet lo mi. of the Belfast Murray Harbor Railway
6. Find +he cost of the lumber for the dre.ssed dnov
facings t.f 30 doors, each 7 ft. high r.iid L'g ft. wide, the
facings being G in. wide, at $18 per M feet.
7. A box whose 1»ase is s(pian! (contains ■• 1 cu. vd.
10 ft. 1)4.3 in., and is 2 ft. .'{ in. iiigh. Find its width.
8. A garden is 24.^ rd. hmg and l.Jj i-d. wide. Kind
the cost of digging a ditch round it 2^ ft. wide by 4 ft.
deep, at G^c. per cubic foot.
9. What will it cost to survey 12 mi. of the Belfast
Railway at $2.2.") a chain ?
of
10. If the diameter
a semicircle I'ornuM
of a circh is 12, what is the area
1 from it V
!M
' 1*JL\( IICAI. J'lJOlJJ.KMS IN Ainni.MKTK
EXCHANGE.
I. Find tlui cost of the f«»lIouiii}r (li-uft, t'xdmiip.
'"'"J^' :} Z l>i-«'iiHum juid iiitcmst G % :—
•*<>««• Clmrlottetown, P.E.T., May 1st, 1902.
Thirty (lays jiftcr si^ht i)ay to W. P. (}uiuly <„•
b.-aivi-, six liundtvd ei^'lity-cijrht dollars, value
received, and charge the same to the aecoiiiit of
<T. J. JMcCornme.
To Royal Bank of Canada, Toronto.
2. Find the co,st of a draft for $174.') on Halifax at
fi % pre iniuni j dso find the cost of the same draft at
i % disc* Hint.
3. How hirge a sight draft on Chicago at } % i>rc-
mium can be jmrchased for $740 ?
4. If £1 stg. exchanges for 24.8 fr., and the Frencli a
per cents are selling at 70.2 fr., what sum of English
money will I pay for 19041 ^ ^; -; of the French 3 i,er cents ?
5. A gentleman in Moncton wishes to pay a bill of
$1400 in St. Paid, Minn. What mnst he pay for a 60-
day draft, exchange being | % preniium and the rate of
discount being 5 % ?
6. Define (a) exchange, (/>) domestic excliange, (e)
foreign exchange, (d) bill of exchange, (e) drawer,
drawee, and payee.
7. A merchant in Liveiix)ol owes a debt of 1750
pistoles to a gentleman in Barcelona. Does he gain or
lose, and how mucb, by sending tlie amornt to
Barcelona by way of France, tlie exchange being
£1 = 24.4 fr., 19 fr. = 1 pistole, ar.d 4 pistoles = £3 ?
8. What is the face of a dr.it on St. Petersburg
wliich can be pmchased for $047.50 when the rouble is
quoted at $.505 ?
P|{A<TI(AI, PifOIU.KMS IN A l.'ITIIM KTlr. \)[
1. If tlio rn|><'<' = $..'{"J.*J, wlmt will !»<* tli.> cost of ii lull
of t'xdmiijye on the Hank of Calcnttii f(»i- LMmX) nii»'«-
Ixnight lit St. Jolm, t-xchanpt Ixinj; 8 % pn'niiniu ?
2. A man h-avinj? ('luirlottctnwn for Sonth Africa
wishes to carry witii liim two l)ills (»f cxclianjr*', one on
a bank in Brazil for ;}00 niilrcis and the other on a bank
in Chili for sncli an amonnt as he can pnrchase with
$282. Find cost of the Prst bill of excluui«re and the
face of tlie hitter, the milreis beinjif (]noted at $M2 and
peso of Cliili ($.91.')) at G % preniinin.
STOCKS.
3. I can olttain $0 more per annnin by investinj^ a
certain snin in 5 per cents at 12S^ than in the 3 per
cents at 81 . Wliat is the snm ?
4. A person laid a certain snm invested in 4 % stock.
Ho sells it at 11 7^, and invests lialf the jiroceeds in 2 %
stock at 90, and the rest in 3 % stock at 99. He tln-n
finds tliat liis annnal income is rednced by .^20. What
anumnt of tlie original stock had lie?
5. I receive an income of $i:n2.r)() fr<»m oOO sliares of
$')() each in a stock comi)any. What is the rate of
dividend?
6. The capital of a mannfactnring concern (consists of
$.j()0(M)() preference stock, paying 4 ', and $70()()(K)
ordinary stock. The Avorking expenses amonut to
$2r)()00 a month, and the receipts average $1000 per
day. Wliat dividend can be declared on tlie ordinary
stock after $24000 is added to a reserve fniid ?
7. If I buy $1000 of 3 % stock at a discount of 3^ y,
sell out again after the stock lias fallen to 82',^, and in-
vest the i>roceeds in 3.^ per cents nt }.;!r, wliat do I
lose in capitad by the whole tian.sjiction ?
'J-' l*IJ.\(TI< ,\l, I'lMHtl.KMs IN A|{||||MKT,( .
1. TF stork hnnfrhtnt 10% pivinium piivs 8" n„ tli.
inv..stnM.nt. what j,,., ..t. w.m.I.I it pav' if lM„.ul.t at
10/^ (liirieouiit y
2. A p. son invests r.n4()0 i„ tlu- H i.c nts sellin-
ut a .liscoui.t of G /. Wli.-u tlMT rise to ir.A 1„. seJJs
.mt $L>()(H)() of Lis stoek, UM,! he sells the re„„.imler when
they have fulle,, to S7J. He then invests the pro. Is
m the r> i,er cents at 108. What does he p,in or lose hv
the transaetioi. ? ''
3. AVlien the 3 tx-:- cents were at !)(). I fouiul that hv
sell.n- out -n<l investing? in Bonjrhton Island 4 peV
cents ..t 9.) I conhl ijicre.ise my in.v.mc l.y £24 ,"'„. Find
tlic amount of my stock in the 8 jx-r cents.
4. A person intending to purchase .Miou^di r, / stock
to yield an in.'on.e of Jfli:,S.:,() p,.,. ,„„„„„ ,,.,,;„ ^,,^.
stock IS at 9."., delays until the ])rice has risen to 055.
How mu<tli more will hv, then have to pay ?
SHARING AND PARTNERSHIP.
5. A, B, and C liad cipuil shares in a Panmure
Island lol.stcr-canninjr estal.lisjiinent. In 1900 they
s<.ld respective'y I ^ aud l 'A their sluires to />, but in
1902 /> retired from business and sold his share in cpial
parts to the ori^ri„al (,wncrs. If J's iuul V\ interest in
the estal.lishmeut is now worth $79:>r),^, what is the
value of /i's share ?
6. A man divides among his sons William. Louis
aud Henry the sum of *948 so that three times the sum
Wdhara receives ecpials five times what Louis gets and
eight times what Henry gets. Divide the money.
^.^••i^*^-
.»■..•*'
PlfArnr \h Pl;<H!l-K.Ms in Aim IM.MKTir. \K
1. A owns J <•( ji vcssfl tiixl /; 111*' iviiijiilidrr: tli
vessel is sold. J ivrei villi,' "0 ' «.f Ms si
a 10% of his- ,1 iitirnvjinl
I.IH' III casll ;i ,ll
s riMM i\,.(l !|<'»(M», niiil the
Vol-
IflU.
Ji u'cnci'nl iiicr
Italancc was tli.-ii iciually dividtd Ix'twrcii ll
how imich was tli<' ,slii|) sold?
2. Fay and Jolmsioii invt'st. capital in
••handise l.usiiifss in tlic proporlion of 4J 1.. (I'/, Aftn-
.'» mo. Fay willwlraws \ oi Ids capifal and Johnston
witlnlniws if of Ids. At tho <'los«^ of tin' year Ihcy have
nad*! in profits ^dCTS. Wliat is ca.-h [>ar*tn.i's share?
:{. John licll s<dd ,'„ of his cslafr, iKvincaflis j; of it to
ids son and if of tlic r.'inaindfr to his wife. Tlic l)ahin.-.'
of it lit' j,dv('s to tluvo pnldic institutions, as follows: To
u hospital he gives $2f):}.S(), to a pnhiic- lil)rary M % less
than he pivo to the Ix.spital, and to a school 20 Z >»i<»rc
than he pive to the library. Find the valne of the estate
4. .1 and D enter into partnership and a^nce to divide
.he in-ofits accordinfjr to tli«^ ea[)ital invested ).y each. A
puts in .l!SJ)() in cash, /.* puts in $(172 in cash and a note at
.'inio. for!i!;]4S. If lh(! note is i)aid at nialnrity how should
an annual profit of !|;70() l»e divided Im-I ween the partners?
"). A and li enter into i»artncrs]iip, ^1 coiitril»utin<,'
$.")()() and /.' $;|()(); iit tlie end of 9 mo. tiny take C as a
partner, who l)iin«rs witli him acaj>ital<.i jfilOOO. The
i>rofit.s, $1()(((), heini; divided ;it the end of aiK.ther 9 mo.,
what .shares did they each rec-ivc?
(J. A iM'i-sou owes .'f!l(t()() to thre<' credit). rs, .1, /,'. jiiid
C. Ilisdel' lo /; is 1.] of wli.-it he owes to T, and liis
del>t to C is ].', of 'vhat he owes to .1. T<t A he {.ays i
of his debt, to /; r of his, and to C },!, of his. flow
nuich does he still
owe
7. Divide .t7(»U(» amon«r fifteen persons so that one
may have $250 more tlian cacli of the otl
iers.
Ill
ANSWKRS
I. •2\ iniinitcH.
». I Ml.-,,..
V\r.v. 7.
2 ir.no; (jnC; lOIOiu'.
n. i'lUMs. Sj,l.; !^,!,:J7.-,.
.'1. m:i*2'>(]( Htii St'.-
<i. 50.
P\(;k 8.
I. 1. 2. (i2.J,..; «2M7.-,. 3. «,,., u.!,.r„H„,,. J.,, ^ ^
... ?lM!»7.-.(). <i. Tl.ufrs. aivcpial tn 7/ •';• ^- .i i : .
7. :i4.Iy. H. §2(M),)!,|t.M,. !i. !,7:j:{.;(H«.<M.>i. io."Jj|(;i ImI^^' v..
1. 58.
I'a«ik 9.
2. hi -joul.rs. -,„!,, Ui^so...to ,aj„.: 2n.in. 13> see. aft..r4a.,n
;;• 30:, /. ». |;t-(i,.25;.<H,n7o-l. r,.Sir,±l7 + . C. twice.
7. .^IHM.21. 8. .().-,
1'/. 17G!J.'):i(;() ill.; J2J.
P. /!E 10
1. A, 1.-. dy.; /;, 10 dy.; r 12, ly.
■^- ^'•»7. 0. 47 II,.
8. )3lfjn!>20; 2(K» ,iii
10. 50 leagues.
9.
II. 10 (.Z.
.'. 700.80. 3. 12.3h-.«78!».
<i. «'!».8(iJ. 7. i ;•;!,',.
>. 4oa2i>l401 l:>0(;o.-,03.-.58 4(M)OOOO.
Paok II.
l-i%f:ain. . 2. 12i%. 3.10.0045.
4. 124 ac. I ro. 1 p.,. :,. r,„.on.-,fi s.|. yd. 0. .OO09187-,
7. 2yr. 4 mo. ISdy. 8. 4 7. ., 3^
10. Len-th, a-2(t.; l.rciultli, l(i ft.; heij,dit, 8 ft' ' "
'1- ■'■'742, •'„ 11,. 1.." •»««"/
la. 105! U s<, yd., 20^
94
Anhnveius.
9.J
Pahr 12.
'•yy*- 2. (fl>MrWA)MI)CCX(|||
•J. »lir. 11 nun. r.\' ] m.-. _,. j- „,
^ ^.-JiifM.. (,. £|7 i&s. «!i,|. i(». ;{2^j.
ft. 2i in.
I. rirrle; 10? J r.l.
J. Hliicksniitli; !ffl l.3:ij.
«i. Og s.,. ft.
I'AilK l.'».
I. $14.40.
5.
!*. 6%.
1'a.;k 14.
i. I %. 3. — .
10. 120 hr.
•• I II Oil II.
7. «I520.
I. 4r.<io II..
Paok 15.
1. «7.40. 2. 1 on. yd. 3. .T,um 1(1, 1J)01, «7 dy.; 8170 -^a
4. 5. ^ 5. A an.l 7/ reciivo 81 1 li a,„| 877i iv,s,Hntively.
«. .677Hf>7142. 7. $235.57.
Paok 16.
1- 125. 2. 834275. .3. 2^1 yr.
f». 82O90».r.I. (5, 400 ft. 7.178332.
!). 822740. 10. 1,7^- ,iii.
4. .Tune 8th, 1901.
H. 3" sq. 1(1.
1 -r^"
Paoe 17.
2. 2.50 11.. 3. 840..3f).
.-.. (a) 2039750, (/,) ;j,|(,:{, (,) 12.4007, {,/) 3789.
7. 8045? times.
4. 12.h', fr.
(>. $H!00.
Paok 18.
1. 16s. 7d. 2. 96. 3. 47.1.5c.
.5. 7.3.44 ft. 6. 24 dy. 7. 8ii«.
9. 889ti.M(i!J.HM..'-.3j.; 40038? 2 L'i <ly.
4. 57? yd.; 86.8a
H. «i In.
if
96
Answeks.
Paoe 19.
1- 40 ft. 2. 3 o'clock.
4. 102 first, .38 second, 100 third.
6. 80.19,V 7. +.
3. 8r)4.28.
5. 5o '/ above cost
8. 292i bhl.
Pack 20.
I. $6.50. 2. 480 rd.
4. $200. 5. 10861578.
7. 54, 51, 48, 39, 36.
3. 18.38 ft. 7 + in.
6. 1 mi. 524 yd.
8. 18|; 3J2.
Page 21.
1. 1260800(X)00. 2. 20 rd. 3, ij.
5. A, fr34; li, $266.40; C, $30G; A $345.60.
7. 2008000. 8. A, 20; /i, .30; C, 50.
9. ^,$384,929; A $250.71; C, $236.36.
4. 7a.
6. 700 sq.ft.
1. -•-
Pace 22.
-2T6. 2. 4568 ft. 3. |.
5. $96. 6. IGghr. 7. $195.
9. $36§ lost.
4. 7.976d.
8. $15.24^
Page 2,3.
1. (a) 117.79 + ft., (f>) 90.97 +ft., (c) 84.71 ft., (d) 9,3.45 ft., (c)
1 13.26 + ft, (/•) 129.74 + ft. 2. $1,304.61+.
3. (a) 12 cu.ft., (/>)864 .sq. ft., (c) 17 ft. nearly. 4. 27i %
^- 26if. 6. 11. Wu. 7. .322830+.
1. A, $8; B,$6.
4. $7176.96.
7. 201.22 ft.
Page 24.
2. 21 sq. yd., 5 sq.ft., 36 sq. in. 3. 302.97 ft.
"'>• 1"3 %gain. 6. $1114.74.
1. S^
2. 72^ ft.
5. o
id. 167 ft. 9+ in.
7. 20 dy.
Page 25.
3. 600. 4. $1280.
6. No; 88 cu. ft. yet du&
8- lo^Ts pure wine.
Ansavtrs.
07
Pa(!K 26.
'''fi. 2. 12 J ft. 3. •'>r,
«742.40. 6.2.^% 7. .5Gft.7|in.
4. .^7.. 50,
K i'4 ft
P.vcJK 27.
$4000gain. 2. 8l.r.7i. 3. . 4. | ac.
■""•^- 6. 45000 qt. ; cheese hy gi7r,() aiid f^ir^oo '
A, 21 dy.; B, 28 dy. 8. 141.062.-3 yd. 9. f «.
Pa«!E 28.
1. 3600.
1.
4.
7.
1.
").
9.
8r,.-,2.08. fi. r>28.03. 7. 5 7 in.
Eastward, 36* 1,5'.
Pa(;k 29.
SI 2000. 2. 24..3474 sq. ft.
3.-) nearly. r,. I3i^ tons.
Gain $132.30. s. 37.476.'J625cu.ft.
•i- 1 M. mi., nearly. 4. 434.26 11>.
•3. .?io.ns.
6. 3(\vt. (ill). 3r)z.
9. 4180680 sq. mi.
Pahk ."JO.
'230.
2. .58.
J780.40. 6. l.-)l69.sq. linb
$464.
3. $-2HH.
7. 12.20.J rd.
10. £-35 las. 4d.
4. $1790.93,'
8. 39 /.
Pa(;k 31.
1.
9.
1.
4.
7.
10.
IG.
2. .00.-)9372.34+,
1 WOSyd. 6. 22» ac.
9^ hr.
3 18s. !,(!.
7. 20 <lv.
MDC.
800080008800080.
4dy. 18hr. 22min. 3
1 yr. 4 mo. 2 i tly.
Pa(jk 32.
2. 1.44.56
5. 81661.2;-..
sec. 8. $300.
11. 871.0.'^
58-1^ dy.
$117.60.
3- 3^ %.
Page .S3.
2. 140^ ton.s.
15. 215.
10. 2jyr.
3. .006.
4. 176.87 sq. yd.
8. 44.21 ft.
3. 8109.
6. 31556160 mil
9. 8725.
4. $23,688.
8. 32.07 + ft.
11. 769,3;, ](,_ ,^,_
446^
A .'lSKt<^^XT^K
08
Answers.
Paoe 34,
1. 1 fur. 1 2 po. 4 yd 1 ft. G in. 2.
I. 78], l()8i 140, 7f>7J. n. 99 yd.
7. $ir,.r)0, ^22.5(t, $ir.. 8. ^\.rti).
'<>• -075%; riu; . 11. «12.54.
3. $1.50.
G. $G0.
9.
Paoe 35,
1. .'')2 sliares, 2, 984| ft.
J. .()0r,[Ki:-2:M+. 5, 37i.
7. 3|min.; lOjiii. aiihour. 8. $17.53.
3. $4.
G. J, §120; J{, $180.
1. 112.G4y(l.
3. ]41G3r>0min,
5. $147.51.
Page 36.
2.
4. —
-; 95 yr.
6. 1820ft.; 195 J sc,. ft.; 60 cu. ft.
Page 37,
1.2 mi, 2. 48 hr. 45 mill. 5 sec. 3, $1020.70, 4. 3lAsq-ft.
5. 3000. 6, 44i5. 7, $8.65 + . 8. 2li"hr.
9, ^,$19.50; ^,$1500, 10, 130 boards; 1040 ft.
1. i
4. 210000 oz,
7, 2552.5.-),
10, I Kit
Page 38,
2. 75 cu, ft,
5, .4, $50; 7?, $240; C, $360.
8. 12 dy,
11. $4752,
3. 39 bu. 42 bu.
G. 128; 2304,
9, $50 loss.
1. 4400 steps; 2i mi,
4. $3.91.
Page 39.
2. lU rolls.
5. $22 gain.
3. 16i%.
6.
1 « 2 3-
I • o 3 a u •
4. 960 ; 44 ; 90 ; 1 50.
7. $317.32.
Page 40.
2. $3501.26 + .
5. 1 /, ft. nearly.
8. $438i.
3. 1 ft.
6. 28034 lb.
■rwmifm-i
Answeiw.
{M.I
1. .
r>. \:i.v,H mi.
8. 900 bbl.
1. 81300.
4. 3450 men
Paoe 41.
2. $127.3,\. 3. $1!).",. 4. 8U.70.
(•>. f 255.-). 52. T. 18 ft. wide hy -') it. loiij;.
9. ^104.23 noaily. lo. .078834 + .
I'a(!k 42.
2. $372.44 A. 3. 18 ft.
__^ 5. 3 i).m. G. ixji.
7. 20000019019; DCV.; 1550. 8. 5900. 9. 500; .002; 0,10.
10. 9.
1. $20.86 + .
4. $20 gain.
7. $420.
Pack 43.
2. 800 trees. 3. $(58.75 increase.
5. 12 boxes. 6. 1 ton 16 cwt. 1 <ir. 5 lb.
8. 87.1792 en. ft.
Tack 44.
1. 62 225 yd. ; 44 yd. 2. 24 mi. 3 fur. 27 pr. 4 yd. 10 in
•*• 1^^'y- 4. $2180. 5. $740. 6(5.
6. $40..50. 7. 416 yd. H. 9.797 ft.
9. $9866. 10. $12576.30 11. 32.2I ft.
1.
5. 33 J.
9. 15c.
I'AfiK 45.
2. $33.60; 15,', cords.
6. 27 U lb.
10. $38.40.
4. 105 mi.
7. £33. 8. .V7;.
Page 46.
1. 30g % on list price ; 36 %. 2. $18.75. 3. $2.5.4.3c. gain.
4. 2068i tiiiies nearly. 5. 11.107 yr. 6. 4 ^"i 7.
7. 3V 8. ■ . 0. $202.50. 10. 3mi.6fur.32;fj.
1. ^^^A.
0. $378.74i.
8. 423.613 + .
P.VGE 47.
2. September 9th. 4. -{ * ? J { .
6. 3 hr. 13 min. 40 sec. 7. £3 17s.
9. 56322. 10. 54.
"^^-"'Mf' ^L ' ii a MJ ' IW ' "-
J 00
Answers.
1.
4.
7.
U.
4.10221140132031.
Pauk 48.
2. $1914.278!) +.
S- 5, -.';'„. 6. £'I ns. 8i(I.
3. r).\d.
"^^^•" '"'• 8. 4 iiiin. 7i sec. imst 3 p.m.
13s. lU.l. nearly. lo. 100.3.003001; 2 -.7. H>787.
Pa(!Z 49.
2. 276 tons. 3. j „i„.s l,y J „ii.
i"). 13801? Eii<,'lisli acres. (!. 1 1 dy.
24 times.
88 f. !;3c.
28.12.J ft.; 7.68
Page 50.
3 ac. 15 [H).; §6.00.
A, 40 ft.; ]}, 30.00 ft.; (',41.42 ft.
28.284 + rd. 6. 1 mi: fur. 27 + rd.
£47 10s. 3d.
8 chaiiis.
§51.33^
Pa(;e 51.
2. 1437 J bricks.
5. $442.47+.
8. May 2 lid.
2. £18 lf).s. 8id.
4. 526^
7. 30 ac. 3 H). 38.88 IK).
3. £.5313 8s. Oid.
6. 64|.
9. $29.02 i.
Page 52.
A, ^V; B, A; C, -,^', D, A. 2. $544.39.
30 mi.
$3 13. 17 A.
f). $1800.
3. 1029.12 ft.
6. $.3.20U.
5 mo.
$03.05.
510 1b.
8. 5.33.43 ft. 9. $3752.95. 10. 108 ft,
Page 53.
2. .300; 56250.
$56.
$0.12.
82Ac.
$2.30.
1.1.
5. 295 boards; $7.09 nearly.
8. $10754.75.
Pv«;k 54.
■2. 51?, 68^ ,3. |.
0. 330 ft. 7. 12;?
Page 55.
2. 4 ac. 20 pn. 26 yd. 81 in.
5. $130. 41c.
8. $152. 9. 66 ft.
3. $3318.05.
0. 32 yd.
4. $0.1192808 +.
3. $9.75.
0. A, $6, n, $4.
10. 2 yr 24 dy.
*?. ^'p,.'\w f /:
ANSWEltij.
101
Paoe 56.
1. 845. 2. 874.8U. 3. ^,83240; />', $1260; (7, 812RO
4.8306.72. 5.28. 6. lOSUi ao. 7. 30 ft.
8. 81200 each loiin.
D. 82JOO to son, $750 to wife, $750 to daughter. 10. 4623^.
Paoe 57.
1. 8270liorse; 870 harness. 2. 35lr.ip3,
3. 8405.90; 25247 H.. 4. Dec. 15,'inOl ; June
13 1 902.
5. 120. 6. 81526.40. 7. $2000.
8. A, $270; //, $280; C, 8310; /),8320. 9. 1720.
Paoe 58.
1. i?. 2. 8150. 3. 8152.37; $152.96. 4. 83566.35.
5. 4i ft. 6. 1280 cattle. 7. $200. 8. 8^ /.
PACiE 59.
1. 89000. 2. 3hr. .3. /I, 8193.55; ^,8206.45. t. 811.57.
5. 42.52+ ft. 6.814812. 7.844.15.
Pack 60.
1.50%. 2.82160. 3. 25 ft., 35 ft. 4. 960 cu. ft.
5. 86703.07. 6. . 7. 8 1 20. 8. 855000.
1. 120 yd.
5. 480.
■2. 895.40.
6. 16 da.
Page 61.
3. 105 IK; 14f%. 4. 840frai,
7. 6s I. in. 8. 216 at;. 9. .,^4%.
Paoe 62.
2. £10 8.S. 3. 84.'».10.
5- JTTTDVfftroff. 6. 52 dy.
7. 14 ® 42c., 3 ® 60c., 4 @ 67c., 22 @ 78c,
1. 4.54 litres,
,1,
4. 2835 cu. in.
8. 72.
ml I ip I I II iMii II .-»=•
102
Aj^sweics.
Pi*oK 63.
MISCELLANEOUS.
1. «9.12. 2. eo 1(5.60 5.
4. A, $2352; /;, $2310.
6. 4dwt. 17?iiijgr.
3. loSuC. in dollar; $1.84^.
r>. loo.iooi.
T. m bu. 8. 3<)2.
Pauk 64.
1-4%.
4. $15. 00.
7. $164.50. i). VAWo
2. $9.09. .3. A, $2.50; Ji, $1.87. J; C, $1.56.
5. $28.57 i. 6. £1 2s. ajd.
1. $8855.04 los.s.
4. £7 16,s. 4d.
Pagis 65.
2. 22i «ly.
5. $375. (!. I
.3. 5.0420168067.
7. 1262.
Pace 66.
1. $5500; $5078i. 2. 7.92 in. .3. 7 dy.
4. 1 11.. feathers, 2 oz. 1 1 .Iwt. ]6 ^r. ; 1 ox. gold heavier Ijy -12.J -r.
6. 1.966. 7. .00054.
9. 64 men.
5. 101.854 +
8. 464
PA(iE 67.
1. 6T,¥/«. 2. 114; X.MC'MLXXXIII. 3. .338500.
4. lOi?; ij)§. .5. 4808880. (! 800.000. 7. 63J.
^' • y- $1«.35. 10. i-;50. 11. 64.521.
Pack 6S.
1. ^1, $47.25; y;, £4.3.80. 2. $40.5o. 3. 621^???. 4. $740.66.
■^- -H«y«l- 6. $2180. 7. . 8. 43,2- |,,
9. A, $640; /i, $840; C, $840. 10. $110.
Pace 69.
1. $7.57J. 2. 1.291875. 3. $19.9U. 4. .'AVA- 7. $12.50.
T"- .jar'-^^.L. 'ix itsaax. t:atijv.
. se^fi^ . f^.-K : "»Tj»: -
Answers.
Paok 70.
(a) 18267.37698. (//) r!8.8616, (r) 1.6.')n26.
(a) 101010, (/>) .M.'-,. 3. .22"23r<.
625?%; 16ii%; 60%. 7. jJi.50.
10 dy
Pace 71.
27 ; .816; .7ry; 8.175; 135.1940625.
54772 4.044; 10.535; 16.104; .06,'?24.
Men, €35 ; women, £56 ; ohilclren, £35.
785. H. 10'," niin.
.2154; 32.1; 4321; 1.357. 10. 168iSJ,gJ.
10.']
4. £62 8.x. 7J(1.
8. 3006 gal.
3. .6875.
6. 33, 18.
Paoe 72.
PROPORTION.
£7 9s. 2. 300. 3. 873i. 4. A, 4; Ti, 3j; C, 2J;
1 hr. 47 min. 23,-, .sec. 6. 180 men.
Soldiers, 9 ac. 12 rd. ; sergeant, 18 jic. 24 rd, ; ensign, 72 .10.
2 rr 16 rd. 11 sec. ; lieutenant, 108 ao. 3 ro. 24 rd. ; cap-
tain, 181 ac. 2 ro. ; major, 272 ac. 1 ro. ; colonel, 458 ac.
3 rd. : $22487.8.5.
Paoe 73.
1.
10.34? a.m.
2. Boy's work is to man's
as 1 is to 3.
3.
2yr.
4. lOlir.
INTEREST AND PERCENTAGE.
5.
17 yr.
6. 9^ %. 7. §762.50.
8. §1? 4.
9.
S78. 50.
Pace 74.
1.
85000.
2. §72.14. 3. §1200.
4. §2851.14.
5.
§1274.50.
6. Fehy. 14th, 1885.
7. §17425.
8.
§35.10.
FRACTIONS.
'
9.
JsisB-
Paoe 75.
1.
.51.
2. ]22,V,-. 3. 2411-
4. 77,^2.
5.
24.28009*^,
6. 2 075645161290322580.
7. 3 times.
8.
50697
2 9 7 3 It •
aismzs"rii~-s:tis.'ii:^€^maa .-. .
104
Answers.
1. $6100.
84!).<t4.
^HUii.Ol.
PAliK 76.
PRESENT WORTH AND DISCOUNT.
|l«809.21.
«7848.ir>+.
7. 70.
$300.
$10000.
86c.
3. $126.18.
7. $100.
4. 84r.
8. $320.62j.
9- 4 %.
Pagk 77.
2. $195,124",. 3. i%l<)88. 4.
«i. $706ii.
STOCKS.
8. $243. 05 + stock. 9. $600000.
Page 78.
2. $1960. 3. $.r;8.31.
5. $19.79j loss. 6. $69418.
8. $16000. 9. 114.
1.
4.
7.
10.
13.
1.
4.
7.
10.
Pagk 79.
MENSURATION.
56 sq. ft. ; none. 2. 645 sii- rd.
$247.15.
li ft. from sides, 4 ft. from ends ; 20g s(]. yd.
3. $146.31i.
$20.95.
61.498 ac.
5 ac. 1 ro. 9 fur.
342.08 sq. yd.
38.51672.
201 J 6u. ft.
477.48 cu. ft.
24428.
20 ^t. nearly.
53 ft.
7. 31 sq. ac. 10 jx). 8. 40.32.
Page 80.
2. 67.74. 3. 6347ift.
5. 553.6.32 sq. ft. 6. 130..381.
8. 106.8144 ft 9. 19.624.
11. 98. 175. 12. 2629J gal.
Page 81.
2. 8.83575 cu. ft. 3. 7.0686 sq. ft
5. 23 ft. nearly. 6. 53 ft.
8. 5.039 in.; 3.78 in. 9. 60^3—.
11. 58.876.
An»vv£Ks.
loo
3. 41.803; 12 ft.
pAor, S'i
I 20 in. 2. 42.5195.
DECIMALS.
4. (n) 2.04.5, (h) d.Ooht\ (r) G9.6H7M3, (,/) H0.738350lA.
5, l«).01397. 6. 1 bu. 2 (it. 1 pt. 7. £31 2s. «ilM
8. 99.84436,
Pack 83.
t. 258.0645 4-. 2. .010418448*.
4. 3 lui. 2 fur. 21 jKt. 4 yd. 1 ft. 6 in.
PROBLEMS RELATING TO WORIC.
«• 3dy. 7. 3dy. 12hr. 46 ■+• inin. 8. $6.40.
3. 48. 4i*7d.
5. .29752.
Paob 84.
1. 849.93i. 2. A, $\G ; B, «;2 ; C, $8.
4. Tom, $18.75; Diik, $15; Harry, $ 1 1.2.5.
7. $372. 8. B, $4; C, $3.
3. 9if dy
5. 2ii dy.
1. 20 :=>«%.
5. 44c.
Paok 85.
PROFIT AND LOSS.
2. He los.s. 3. 60%. 4. 18|%gain.
6. 85? %. 7. $272.34? gain. 8. $.386.86.
Pace 86.
1. $26.47 nearly, lost. 2. 2?c. on the $. 3. $261056,^0 nearly.
4. $584.
TAXES AND DUTIES.
6. $7200; $675.
Page 87.
1. 82. r/ nearly. 3. $3^^1.89 ,V 4. $18.55 +. 5. 6^ %.
<« $1394 nearly. 7. $26000.
um
ANSWKUfti.
I. $31.04.
Padk 88.
SQUARE AND CUBE ROOTS.
•2. 7(M)4Hli4. 3. 8.027 an.l .(J064.
1 _
<i ,„ f4.(m(i, (2.403)', v^''.^7.iyo625:
> »
s. 35.8 + in. 10. 1!). 11. |.
iW,»*
7. «i.ir.
2. 7.
Paok 89.
MEASUREMENTS.
3. Circle. 4. lua ft. .'>. 3s)601 hIccikts; 132(XK)0 11.. in-n
6. «<!>.54. 7. 3 yd. 2 ft. 8 ill. 8. $185,301. 0. f lOM)
10. 66.548 +. ' . '
Pacik 90.
EXCHANGE.
2. $1747.18; $1740.04. 3. $740.44. 4. £53U.
I. $08.M,3.
5. $l38y.50. 7. £3 83. lojd.
8. 1148»0l roubles.
1. I!?697.68.
3. $.3078.
1. yJ 7o-
5. $404 4 ^
Paoe 91.
2. $168.00; 300.35 jieso.
STOCKS.
4. $200O. 5. 5i%. 0.3%. 7. $141.2a.
Paoe 92.
2. $700. 3. £3078. 4. $173.92*.
SHAPING AND PARTNERSHIP.
8. W., $840; L., $288; H., $180.
Paoe 93,
i. $35000. 2. F., $3870.09; J., $2807.31. 3. $.•J847.s.^
4. A, $357.20; ^$348.80. 5. $384.61 A, $230.76tif, .I3.s4.6l iV-
6. $600. 7. $700 to one, J?450 to each of t! ? others.
*