Charles Davies.

# School arithmetic. Analytical and practical online

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Font size 11. Multiply 38049.079 by 0.00008.

12. What will 6.29 weeks' board come to at 2.75 dollars
per week ?

13. What will 61 pounds of sugar come to at \$0.234 per
pound ?

209. After multiplying, how many decimal places will you point off
In the product ? When there are not so many in the product what do
you do ? Give the rule for the multiplication of decimals.

192

CONTRACTIONS.

14. If 12 . 836 dollars are paid for one barrel of flour, what
will . 354 barrels cost ?

15. What are the contents of a board, . 06 feet long and . 06
wide?

16. Multiply 49000 by .0049.

17. Bought 1234 oranges for 4 . 6 cents apiece : how much
did they cost ?

18. What will 375.6 pounds of coffee cost at .125 dollars
per pound ?

19. If I buy 36. 251 pounds of indigo at \$0.029 per pound,
what will it come to ?

20. Multiply \$89. 3421001 by .0000028.

21. Multiply \$341.45 by .007.

22. What are the contents of a lot which is . 004 miles long
and . 004 miles wide ?

23. Multiply .007853 by .035.

24. What is the product of \$26.000375 multiplied 1>v
.00007?

CONTRACTIONS.

210. When a decimal number is to be multiplied by 10,
100, 1000, &c., the multiplication may be made by removing
the decimal point as many places to the right hand as there
are ciphers in the multiplier, and if there be not so many
figures on the right of the decimal point, supply the deficiency
by annexing ciphers.

Thus, 6.79 multiplied by -

10

100
1000
10000
100000

Also, 370 . 036 multiplied by

flO 1

|100

1000 L =

10000
100000 J

67.9

679

6790

67900

679000

3700.36
37003.6
370036
3700360
37003600

210. How do you multiply a decimal number by 10, 100, 1000, Ac. ?
If there are not as many decimal figures as there are ciphers in the
multiplier, what do you <lo ?

DECIMAL FRACTIONS. 193

DIVISION OF DECIMAL FRACTIONS.

211. Division of Decimal Fractions is similar to that of
simple numbers.

1. Let it be required to divide 1.38483 by 60.21.

ANALYSIS. The dividend must be equal OPERATION.

to the product of the divisor and quotient, 60 . 21 ) 1 . 38483(23
(Art, 61) ; and hence must contain as j 2042

many decimal places as both of them ;
therefore,

There, must be as many decimal places in 18063

the quotient as the decimal places in the divi- ~r~ 7\wi

dend exceed those in the divisor : hence,

R.ULE. Divide as in simple numbers, and point off" in the
quotient, from the right hand, as many places for decimals as
the decimal places in the dividend exceed those in the divisor ;
and if there are not so many, supply the deficiency by prefix-
ing ciphers.

EXAMPLES.

1. Divide 2.3421 by 2.11

2. Divide 12.82561 by 3.01.

3. Divide 33.66431 by 1.01.

4. Divide .010001 by .01.

5. Divide 8.2470 by .002.

6. Divide 94.0056 by .08.

7. What is the quotient of 37 . 57602, divided by 3 ; by . 3 ;
by .03; by .003; by .0003?

8. What is the quotient of 129.75896, divided by 8 ; by
.08; by .008; by .0008; by .00008?

9. What is the quotient of 187 .29900, divided by 9 ; by
.9 ; by .09 ; by .009 ; by .0009 ; by .00009 ?

10. What is the quotient of 764 2043244, divided by 6 ;
by .06 ; by .006 ; by .0006 ; by .00006 ; by .000006?

NOTE. 1. When there are more decimal places in the divisor
than in the dividend, annex ciphers to the dividend and make the
decimal places equal ; all the figures of the quotient will then be
whole numbers.

211. How docs the number of decimal places in the dividend com-
pare with that in the divisor and quotient? How do you determine
the number of decimal places in the quotient? If the divisor contains
four places and the dividend six, how many in the quotient ? If the
divisor contains three places and the dividend five, how many in the
quotient ? Give the rule for the division of decimals.
13

DIVISION OF

EXAMPLES.

1. Divide 4397. 4 by 3. 49.

NOTE. We annex one to
no decimal place we should
have annexed two.

OPERATION.
3.49)4397.40(1260
349

907
698

2094
2094

An*. 1260.

2. Divide 2194.02194 by .100001.

3. Divide 9811. 0047 by .325947.

4. Divide .1 by .0001. | 5. Divide 10 by .15.

6. Divide 6 by .6 ; by .06 ; by. 006 ; by .2 ; by .3 ; by
.003; by .5; by .05; by .005.

NOTE. 2. When it is necessary to continue the division farther
than the figures of the dividend will allow, we annex ciphers, and
consider them as decimal places of the dividend.

When the division does not terminate, we annex the plus sign
to show that it may be continued : thus .2 divided by ^=.666+.

EXAMPLES.

1. Divide 4. 25 by 1.25.

ANALYSIS. In this example we annex one 0.
and then the decimal places in the dividend will
exceed those in the divisor by 1.

OPERATION.

25)4.25(3.4

3.75

~500

500

Ans. 3.4.

2. Divide . 2 by .6.

3. Divide 37. 4 by 4. 5.

4. Divide 586.4 by 375.

5. Divide 94 . 0369 by 81 . 032.

NOTE. 3. When any decimal number is to be divided by 10,
100, 1000, &c., the division is made by removing the decimal
point as many places to the left as there are Q's in Vie divisor ; and
if there be not so many figures on the left of the decimal point,
the deficiency is supplied by prefixing ciphers.

27 . 69 divided by

10
100
1000
10000

2.769
.2769
.02769
.002769

DECIMAL FRACTIONS. 195

10

100

642.89 divided by -I 1000
10000
100000

64.289
6.4289
.64289
.064289
.0064289

QUESTIONS IN THE PRECEDING RULES

1. If I divide .6 dollars among 94 men, how much will

2. I gave 28 dollars to 267 persons : how much apiece ?

3. Divide 6 35 by .425.

4. What is the quotient of \$36.2678 divided by 2.25 ?

5. Divide a dollar into 12 equal parts.

6. Divide .25 of 3.26 into .034 of 3.04 equal parts.

7. How many times will .35 of 35 be contained in .024
of 24? *

8. At .75 dollars a bushel, how many bushels of rye can
be bought for 141 dollars ?

9. Bought 12 arid 15 thousandths bushels of potatoes for
33 hundredths dollars a bushel, and paid in oats at 22 hun-
dredths of a dollar a bushel : how many bushels of oats did it
take?

10. Bought 53.1 yards of cloth for 42 dollars : how much
was it a yard ?

11. Divide 125 by .1045.

12. Divide one millionth by one billionth.

1 3. A merchant sold 4 parcels of cloth, the first contained
127 and 3 thousandths yards ; the 2d, 6 and 3 tenths yards ;
the 3d, 4 and one hundredth yards ; the 4th, 90 and one
millionth yards : how many yards did he sell in all ?

14. A merchant buys three chests of tea, the first contains
60 and one thousandth pounds ; the second, 39 and one ten
thousandth pounds ; the third, 26 and one tenth pounds : how
much did he buy in all ?

NOTE. 1. If there are more decimal places in the divisor than in the
dividend, what do you do ? What will the figures of the quotient then
be?

2. How do you continue the division after you have brought down all
the figures of the dividend ? What sign do you place after the quo-
tient ? What does it show?

3. How do you divide a decimal fraction by 10, 100, 1000, &c. ?

19G DIVISION OF

15. What is the sum of \$20 and three hundredths ; \$4
and one-tenth, \$6 and one thousandth, and \$18 and one
hundredth ?

16. A puts in trade \$504.342 ; B puts in \$350.1965 ; C
puts in \$100.11; D puts in \$99.334; and E puts in
\$9001.32 : what is the whole amount put in ?

It. B has \$936, and A has \$1, 3 dimes and 1 mill : how
much more money has B than A ?

18. A merchant buys 37.5 yards of cloth, at one dollar
twenty-five cents per yard : how much does the whole
come to ?

19. If 12 men had each \$339 one dime 9 cents and 3
mills, what would be the total amount of their money ?

20. A farmer sells to a merchant 13.12 cords of wood at
\$4.25 per cord, and 13 bushels of wheat at \$1.06 per bushel :
he is to take in payment 13 yards of broadcloth at \$4.07 per
yard, and the remainder in cash : how much money did he

21. If one man can remove 5.91 cubic yards of earth in a
day, how much could nineteen men remove ?

22. What is the cost of 8.3 yards of cloth at \$5.47 per
yard?

23. If a man earns one dollar and one mill per day, how
much will he earn in a year of 313 working days ?

24. What will be the cost of 375 thousandths of a cord of
wood, at \$2 per cord ?

25. A man leaves an estate of \$1473.194 to be equally
divided among 12 heirs : what is each one's portion ?

26. If flour is \$9.25 a barrel, how many barrels can I buy
for \$1637.25 ?

27. Bought 26 yards of cloth at \$4.37| a yard, and paid
for it in flour at \$7.25 a barrel : how much flour will pay
for the cloth ?

28. How much molasses at 22|- cents a gallon "must be
given for 46 bushels of oats at 45 cents a bushel?

29. How many days work at \$1.25 a day must be given
for 6 cords of wood, worth \$4.12| a cord?

30 What will 36.48 yards of cloth cost, if 14.25 yards
cost \$21. 375?

31. If you can buy 13.25/6. of coffee for \$2.50, how much
can you buy for \$325.50 ?

DECIMAL FRACTIONS.

197

212. To change a common to a decimal fraction.

The value of a fraction is the quotient of the numerate!
divided by the denominator (Art. 148).

1. Reduce J to a decimal.

If we place a decimal point after the 5, and then OPERATION.
write any number of O's, after it, the value of the 8)5.000
numerator will not be changed (Art. 205). T'9f\

If, then, we divide by the denominator, the quo-
tient will be the decimal number : hence,

RULE. Annex decimal ciphers to the numerator, and
then divide by the denominator, pointing off as in division
of decimals.

1 . tteduce

EXAMPLES.

to its equivalent decimal.

We here use two ciphers, and therefore point
off two decimal places in the quotient,

Reduce the following" fractions to decimals

OPERATION.

125)635(5.08
625
1000
1000

to a decimal.

1. Reduce -^ to a decimal.

2. Reduce -J-f- to a decimal.

3. Reduce -fa to a decimal.

4. Reduce J and t ^ 5 .

5. Reduce ^5-, f f , and

6. Reduce J and
V. Reduce

8. Reduce f,

9. Reduce to a decimal.

213. A decimal fraction may be changed to the form of a
vulgar fraction by simply writing its denominator (Art. 202).

212. How do you change a vulgar to a decimal fraction ?

213. How do you change a decimal to the form of a vulgar fraction ?

10. Reduce

11. Reduce

12. Reduce

13. Reduce

14. Reduce T

15. Reduce

16. Reduce

17. Reduce

18. Reduce

198 DENOMINATE DECIMALS.

EXAMPLES.

1. What vulgar fraction is equal to .04 ?

2. What vulgar fraction is equal to 3.067 ?

3. What vulgar fraction is equal to 8.275 ?

4. What vulgar fraction is equal to .00049 ?

DENOMINATE DECIMALS.

214. A denominate decimal is one in which the unit of the
fraction is a denominate number. Thus, .5 of a pound, .6 of a
shilling, .7 of a yard, &c., are denominate decimals, in which
the units are 1 pound, 1 shilling, 1 yard.

CASE I.

215. To change a denominate number to a denominate
decimal.

1. Change 9tf. to the decimal of a .

ANALYSIS. The denominate unit of the frac- OPERATION.

tion is l=24Qd. Then divide Qd. by 240: 2Qd.=l

the quotient, .0375 of a pound is the value of 240) 9 (.03 7 5

9dJ. in the decimal of a : hence, ^ . ^ 0375

RULE. Reduce the unit of the required fraction to the unit
of the given denominate number, and then divide the denomi-
nate number by the result, and the quotient will be the decimal.

EXAMPLES.

1. Reduce 7 drams to the decimal of a Ib. avoirdupois.

2. Reduce 26d. to the decimal of a .

3. Reduce .056 poles to the decimal of an acre.

4. Reduce 14 minutes to the decimal of a day.

5. Reduce 21 pints to the decimal of a peck.

6. Reduce 3 hours to the decimal of a day.

7. Reduce 375678 feet to the decimal of a mile.

8. Reduce 36 yards to the decimal of a rod.

9. Reduce .5 quarts to the decimal of a barrel.

10. Reduce .7 of an ounce, avoirdupois, to the decimal of a
hundred.

214. What is a denominate decimal ?

215. How do you change a denominate number to a denominate
decimal ?

DENOMINATE DECIMALS. 199

CASE II.

216. To find the value of a decimal in integers of a less
denomination.

1. Find the value of .890.625 bushels.

OPERATION.

ANALYSIS. Multiplying the decimal by 4, (since 4 890625

pecks make a bushel), we have 3,5625 pecks. Mul- \

tiplying the new decimal by 8, (since 8 quarts make __ _

a peck), we have 4.5 quarts. Then, multiplying 3.562500

this last decimal by 2, (since 2 pints make a quart), 8

we have 1 pint; hence, 4.500000

2

_

. Bpk. Iqts. Ipt. 1.000000

RULE. I. Multiply the decimal by that number which
will reduce it to the next less denomination, pointing off as
in multiplication of decimal fractions.

1 1 . Multiply the decimal pa rt of the product as before ; and
so continue to do until the decimal is reduced to the required
denominations. The integers at the left form the answer.

EXAMPLES.

1. What is the value of .002084/6. Troy?

2. What is the value of . 625 of a cwt. ?

3. What is the value of . 625 of a gallon ?

4. What is the value of . 3375 ?

5. What is the value of . 3375 of a ton ?

6. What is the value of . 05 of an acre ?

7. What is the value of . 875 pipes of wine ?

8. What is the value of .125 hogshead of beer ?

9. What is the value of . 375 of a year of 365 days ?

10. What is the value of . 085 of a ?

11. What is the value of .86 of a cwt. ?

12. From .82 of a day take .32 of an hour.

13. What is the value of 1.089 miles?

14. What is the value of .09375 of a pound, avoirdupois ?

15. What is the value of .28493 of a year of 365 days ?

16. What is the value of 1.046?

17. What is the value of 1.88 ?

216. How do you find the value of a decimal in integers of a less
denomination ?

200 DENOMINATE DECIMALS

CASE III.

217. To reduce a compound denominate number to a
decimal or mixed number.

1. Reduce 1 4s. 9|c?. to the decimal of a .

ANALYSIS. Reducing the f<f. to a decimal
(Art. 215), and annexing the result to the 9d, * ? _ I ^

we have 9.75d. Dividing 9 .75d. by 12, (since \$T~~ '
12 pence Is.), and annexing the quotient to y\$d. = \$ .*l5d.
the 4s. we have 4.8125s. Then, dividing by 20 12)9 75c?
(since 20s.=l,) and annexing the quotient
to the 1, we have 1.240625 :

Ans. 1 4s. 9|d. = 1.240625.

RULE. Divide the lowest denomination by as many units
as make a unit of the next higher, and annex the quotient
as a decimal to that higher: then divide as before, and so
continue to do until the decimal is reduced to the required
denomination.

EXAMPLES.

1. Reduce kwk. \$da. 5/ir. 30m. 45s, to the denomination
of a week.

2. Reduce 2/6. 5oz. I2pwt. Iftgr., to the denomination of a
pound.

3. Reduce 3 feet 9 inches to the denomination of yards.

4. Reduce 1/6. 12dr., avoirdupois, to the denomination of
pounds.

5. Reduce 5 leagues 2 furlongs to the denomination of
leagues.

6. Reduce 46u. %pk. 4=qt. Ipt. to the denomination of
bushels.

7. Reduce 5oz. ISpwt. I2gr. to the decimal of a pound.

8. Reduce Ibcwt. 3qr. 2J/6. to the decimal of a ton.

9. Reduce 5A 3/?. 21sg. rd. to the denomination of acres.

10. Reduce 11 pounds to the decimal of a ton.

1 1. Reduce 3efa. l%%xcc. to the decimal of a week.

12. Reduce 146w. 3%qt. to the decimal of a chaldron.

13. Reduce 7m. 7/wr. Ir. to the denomination of miles.

217. How do you reduce a compound denominate number to
a decimal V

ANALYSIS. 201

ANALYSIS.

218. An analysis of a proposition is an examination of its
separate parts, and their connections with each other.

The solution of a question, by analysis, consists in an exami-
nation of its elements and of the relations which exist between
these elements. We determine the elements and the rela-
tions which exist between them, in each case, by examining
the nature of the question.

In analyzing, we reason from a given number to its unit,
and then from this unit to the required number.

EXAMPLES.

1. If 9 bushels of wheat cost 18 dollars, what will 21
bushels cost ?

ANALYSIS. One bushel of wheat will cost one ninth as much as
9 bushels. Since 9 bushels cost 18 dollars, 1 bushel will cost ^
of 18 dollars, or 2 dollars; 27 bushels will cost 27 times as much
as 1 bushel : that is, 27 times ^ of 18 dollars or 54 dollars.

OPERATION.

18

O>7 V <**

=\$54 ; Or,

'

| 54 .4ns.

NOTE. 1. We indicate the operations to be performed, and
then cancel the equal factors (Art. 141).

219. Although the currency of the United States is ex-
pressed in dollars cents and mills, still in most of the States
the dollar (always valued at 100 cents), is reckoned in shil-
lings and pence ; thus,

In the New England States, in Indiana, Illinois, Missouri, Vir
ginia. Kentucky, Tennessee, Mississippi and Texas, the dollar is
reckoned at G shillings: In New York, Ohio and Michigan, at 8
shillings: In New Jersey, Pennsylvania, Delaware and Mary
land, at 7s. 6d. : In South Carolina, and Georgia, at 4s. 8d. : In
Canada and Nova Scotia, at 5 shillings.

21S. What is an analysis ? In what does the solution of a question
by analysis consist ? How do we determine the elements and their
relations ? How do we reason in analyzing V

202

ANALYSIS.

NOTE In many of the States the retail price of articles is given
in shillings and pence, and the result, or cost, required in dollars
and cents.

2. What will 12 yards of cloth cost, at 5 shillings a yard,
New York currency ?

ANALYSIS. Since 1 yard cost 5 shillings 12 yards will cost 12
times 5 shillings, or 60 shillings and as 8 shillings make 1 dollar,
New York currency, there will be as many dollars as 8 is contain-
ed timesin60=\$7ir.

OPERATION.

5xl2-^8=\$7.50; Or,

n

5

2 | 15 = ^=\$7.50.
\$!.50.

NOTE. The fractional part of a dollar may always be reduced
to cents and mills by annexing two or three ciphers to the nume-
rator and dividing by the denominator ; or, which is more conve-
nient in practice, annex the ciphers to the dividend and continue
the division.

3. What will be the cost of 56 bushels of oats at 3s Zd a
bushel, New York currency ?

OPERATION.

Or,

4 | 91

\$22.75 Am.

NOTE. When the pence is an aliquot part of a shilling the
price may be reduced to an improper fraction, which will be the
multiplier: thus, 8l 8d.=8i*.= 1 /. Or: the shillings and pence
may be reduced to pence; thus, 3s 3d. ~39rf., in which case the,
product will be pence, and must be divided by 96, the number of
pence in 1 dollar : hence,

220. To find the cost of articles in dollars and cents.

219; In what is the currency of the States expressed ?
the currency of the States often reckoned ?
220. How do you find the cost of a commodity ?

In what is

ANALYSIS. 203

Multiply the commodity by the price and divide theprodutc
by the value of a dollar reduced to the same denominational
unit.

4. What will 18 yards of satinet cost at 3s. d. a yard,
Pennsylvania currency ?

OPERATION.

Or, * 00

\ \$y. | \$9 Ans.

NOTE. The above rule will apply to the currency in any of
the States. In the last example the multiplier is 3s. 9c?.=3J*.
=J*. or 46d. The divisor is 7*. W.=7|*.=^f.=90tl,

5. What will 7J/6. of tea cost at 6s. Sd. a pound, New
Englan4 currency ?

OPERATION.

t

t\$ L 5

**n

*}*

3*

20 l Or,

00

3

25

6. What will be the cost of 120?/^s. of cotton cloth at Is.
f)d. a yard, Georgia currency ?

7. What will be the cost in New York currency ?

8. What will be the cost in New England currency ?

9. What will be the cost of 75 bushels of potatoes at 3s.
6d., New York currency ?

10. What will it cost to build 148 feet of wall at Is. Sd.
per foot, N. Y. currency ?

11. What will a load of wheat, containing 46 J bushels
come to at 10s. Sd. a bushel, N. Y. currency?

12. What will 7 yards of Irish linen cost at 3s. 4d. a yard,
Pcnn. currency ?

13. Kow many pounds of butter at Is. 4d. a pound must
be given for 12 gallons of molasses at 2s. Sd. a gallon ?

204

ANALYSIS.

12

OPERATION.

Or,

12

24/6.

| 24/6.

NOTE. The same rule applies in the last example as in the
preceding ones, except that the divisor is the price of the article
received in payment, reduced to the same unit as the price of the
article bought.

14. What will be the cost of 12cwt. of sugar at 9cZ. per /&.
N. Y. currency?

OPERATION.

25
9

2 225

NOTE. Reduce the cicts. to Ibs. by
multiplying by 4 and then by 25. Then 2 ^
multiply by the price per pound, and
then divide by the value of a dollar in
the required currency, reduced to the
same denomination asjthe price.

Ans. \$112,50

15. What will be the cost of 9 hogsheads of molasses at Is.
3d. per quart, N. E. currency ?

16. How many days work at 7s. 6c?. a day must be given
for 1 2 bushels of apples at 3s. \$d. a bushel ?

17. Farmer A exchanged 35 bushels of barley, worth 6s.
4d. t with farmer B for rye worth 7 shillings a bushel : how
many bushels of rye did farmer A receive ?

18. Bought the following bill of goods of Mr. Merchant :
what did the whole amount to, N. Y. currency ?

12| yards of cambric at Is.

8 " ribbon

21 " calico

6 " alpaca

4 gallons molasses

2J pounds tea
30 " sugar

19. Iff of a yard of cloth cost \$3.20, what will -}- of a
yard cost ?

ANALYSIS. Since 5 eighths of a yard of cloth costs \$3,20, 1 eighth
of a yard will cost i of \$3,20 ; and 1 yard, or 8 eighths, will cost
8 times as muck, or of \$3,20, |\$ of a yard will cost i as much
as 1 yard, or i\$ of of \$3.20= \$4.80.

4d per yard.
2s. 6d. "
Is. 3d. "
5s. Qd, "
3s. bd. per gallon.
6s. 6c?. per pound.

ANALYSIS. 205

OPERATION.

1.60 , * yi

*.20xlx?xi?=\$4.SO. Or,

& 1 40

\$4.80.

20. If 3 j pounds of tea cost 3^ dollars, what will 9 pounds
cost?

NOTE. Reduce the mixed numbers to improper fractions, and
then apply the same mode of reasoning as in the preceding ex-
ample.

21. What will 8| cords of wood cost, if 2f cords cost 7J-
dollars ?

22. If 6 men can build a boat in 120 days, how long will
it take 24 men to build it ?

ANALYSIS. Since 6 men can build .a boat in 120 days, it will
take 1 man 6 times 120 days, or 720 days, and 24 men can build
it in fa of the time that 1 man will require to build it, or fa of G
times 120, which is 30

OPERATION.

30
120x6 -=-24 = 30 days. Or,

M

Ans. 30 days,

23 If 7 men can dig a ditch in 21 days, how many men
will be required to dig it in 3 days ?

24. In what time will 12 horses consume a bin of oats,
that will last 21 horses 6f weeks ?

25. A merchant bought a number of bales of velvet, each
containing 129^ yards, at the rate of 7 dollars for 5 yards,
and sold them at the rate of 1 1 dollars for 7 yards ; and
gained 200 dollars by the bargain : how many bales were
there ?

ANALYSTS Since he paid 7 dollars for 5 yards, for 1 yard he
paid ^ of \$7 or I of 1 dollar ; and since he received 11 dollars for
7 yards, for 1 yard he received | of 11 dollars or V- of 1 dollar
He gained on 1 yard the difference between and V~= - 3 5 r of a dol
lar. Since his whole gain was 200 dollars, he had as many yards
as the gain on one yard is contained times in his whole gain, or
as :ft, is contained times in 200. And there were as many bales
as 129 1^, (the number of yards in one bale), is contained times in
the whole number of yards ^^ ; which gives 9 bales.

206 ANALYSIS.

OPERATION.

= 3500, number of yards in a bale : *

<&

-=-^ 6 5=- 2 -% - -, whole number of yards: ^00

LAO_0 -9 K~l \$\$00

200

*

26. Suppose a number of bales of cloth, each containing
133^ yards, to be bought at the rate of 12 yards for 11 dol-
lars, and sold at the rate of 8 yards for 7 dollars, and the
loss in trade to be \$100 : how many bales are there ?

27. If a piece of cloth 9 feet long and 3 feet wide, contain
3 square yards ; how long must a piece of cloth that is 2f
feet wide be, to contain the same number of yards ?

28. A can mow an acre of grass in 4 hours, B in 6 hours,
and C in 8 hours. How many days, working 9 hours a day,
would they require to mow 39 acres ?

ANALYSIS. Since A can mow an acre in 4 hours, B in 6 hours,
and C in 8 hours, A can mow ^ of an acre, B ^ of an acre, and
C ^ of an acre in 1 hour. Together they can mow i-ri+|=H
of an acre in 1 hour. And since they can mow 13 twenty-fourths
of an acre in 1 hour, they can mow 1 twenty fourth of an acre
in ^ of 1 hour ; and 1 acre, or f^, in 24 times -jV ^f,- of 1 hour
and to mow 39 acres, they will require 39 times ^ ^ hours,
which reduced to days of 9 hours each, gives 8 days.

OPERATION.

l-H+!=Mhours.

8 \$ n

v* x yX0 = 8 days. Or, \$

\$ Am. \ 8 days.

29. A can do a piece of work in 4 days, and B can do the

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