23. If a cistern of 171 feet long, 101 broad, and 13 deep, hold 546 barrels, of water, how many barrels will fill a cistern that is 16 feet long, 7 broad, and 15 deep?

Ans. 384.

24. Lent a friend $292 for 6 months; some time after, he lent me $806; how long may I keep it to balance the favour?

Ans. 2mo. 6d.

25. How many pears can I have for $1.35, if 70 chesnuts are worth 50 almonds, and 48 almonds 1 pomegranate, and 28 lemons 18 pomegranates, and 25 pears 10 lemons, and 108 chesnuts cost 24 cents? Ans. 375. 26. If 21 men could perform a work in 17 days, and 16 men be added to them after the second day, how much time will be saved by it?

Ans. 61 days. 27. If 12 shoemakers, in 2 weeks, make 36 pair of men's and 24 pair of women's shoes; how many pair of each sort, would 18 shoemakers make in 5 weeks? Ans. 135 pair of men's, and 90 pair of women's. 28. If A raises goods worth $30 to $40 and gives 9 months credit, how high must B raise goods worth $27 to give 10 months credit? Ans. $37. 29. A wall was to be built 700 yards long in 29 days; and after 12 men had worked 11 days, they had completed only 220 yds.; how many men must be added to finish it in the time proposed?

Ans. 4.

30. A ship's crew of 300 men, are provided with provisions for 12 months, so that each man is allowed 30 oz. per day; but having been 6 months on their voyage, they find it will take 9 months more before they can finish it, and having lost 50 of their number, it is required to find the daily allowance of each man during the last 9 months. Ans. 24 ounces.

PRACTICE.

175. Practice is a contraction of the RULE OF THREE, when the first term happens to be a unit.

176. One number is said to be an ALIQUOT PART of another, when it exactly measures that other number.

Thus, 25 cents is an aliquot part of 1 dollar, because 25 cents exactly measures 1 dollar; that is, it is contained just 4 times in i dollar. 4 months is an aliquot part of 1 year, because it is contained just 3 times in 1 year, &c.

177. 1. What is the cost of 1576yds. at $ .333 per yard?

Were the cloth $1 per yard, it is plain, it would cost just as many dollars as there are yards, viz. $1576; consequently, the cost of it at 334 cents (of a dol lar), will be as much, that is, 3)1576 $525.33}, Ans.

2. What is the cost of 1262 yards at $.75 per yard?

$946.50" at 75 cents, Ans. sum of these two, viz., the cost at 50 cents and $946.50, Ans.

At $1 per yard, it would be $1262;-at 50 cents it would be

as much, that is $631. But the price is 75 cents, that is, 25 cents more than 50. The cost at 25 cents, it is evident, would be

as much as at 50 cents, that is, $315.50. And it is plain, that the cost at 75 cents, will be the at 25; that is $631 +$315.50

3. What is the cost of 3746yds, at 4d. per yard?

The cost at 1s. per yard would be 37468.; hence the cost at 4d. will be as much.

4. What is the cost of 4937yds. at 9d. per yard?

Ans. £62, 8s. 8d.

It is evident that the cost at 6d. and at 3d. added together will be the cost at 9d.

5. What is the cost of 473yds. at 6s. 8d. per yard?

69. 8d. of a pound.

Ans. £185, 28. Id.

Ans. £157, 138. 4d.

178. 6. What is the cost of 287yds. at 7s. 6d. per yard?

287yds. at £1=

The cost at 10s., it is evident, will be as much as the cost at £1; the cost at 5s. will be as much as the cost at 10s.; and the cost at 2s. 6d. will be as much as the cost at 5s. And it is also evident, that the cost at 10s., at 5s., and at 2s. 6d. added together, will be the cost at (10s. 6d.+58.+2s. 6d. =) 17s. 6d.

287£

6

Ans. £251

2

7. What is the cost of 146yds. at 14s. 9d. per yard?

8. What cost 218 yds. at 12s. 6d. per yard? 9. What cost 156yds. at £3, 6s. 8d. per yard? be £468.)

Ans. £107, 13s. 6d. Ans. £136, 11s. 3d. (The price at £3 would Ans. £520.

10. What cost 9993 tons, at £19 19s. 11d. 3qrs. per ton?

Ans. £19992, 6s. 5ad.

THEORETICAL QUESTIONS. What is practice? When is one number said to be an aliquot part of another?

INTEREST.

179. Interest is an allowance made for the use of money. It is computed at a certain RATE PER CENT.; that is at a certain number of dollars for each hundred dollars, or at a certain number of pounds for each hundred pounds, &c.*

The rate established by law in New-England is 6 per cent.; that is, $6 are allowed for each $100, 6 cents for each 100 cents, £6 for each £100, and so on; in other words,

6 of the sum LENT or DUE is allowed for the use of it ONE

100

YEAR.

In New-York the rate established by law is 7 per cent.; that is, in New-York of the sum lent or due is allowed for the use of it

one year.

* And is understood to be PER ANNUM, that is, by the year.

SUPPOSE THE SUM LENT OR DUE TO BE $1.

In New-England the interest of it for 1 year, would be of a dollar; that is, 6 cents, which expressed decimally, would be

In New-York it would be

And so of any other rate per cent.

$.06 .07

180. PER CENT. signifies by the hundred; rate per cent. is, therefore, a decimal carried to TWO PLACES. than hundredths are parts of one per cent.

All rates lower

.01

.005

.0025

.0075

9 per cent.?

-84 per cent.?

94 per cent.?

10 per cent. ?

10 per cent.?

per cent. is 3 times 4 per cent., that is,

10 per cent. ? 12 per cent.?

181. PRINCIPAL is the money at interest. 182. AMOUNT is the principal and interest.

1. What is the interest of $19 for 1 year at 6 per cent.?

The interest of $1 for 1 year is $.06, that is 6 cents; consequently the interest of $19 will be 19 times as much, that is, 19 times .06; or, which is the same thing, .06 times 19. Thus,

$19
.06

$1.14

183. Hence to find the interest of any sum for 1 year, we have this RULE.-Multiply it by the RATE PER CENT. written as a DECIMAL FRACTION.

2 What is the interest of $72.15 for one year at 3 per cent.?

$72.15 .035 36075 2 1645

$2.52525

Here are five decimal places in the factors; therefore we point off five places for decimals in the product, and obtain for the answer $2, 52 cents, 5 mills, and 25 of a a mill. The parts of a mill are generally disregarded as of no material value.

per cent. ?

3. What is the interest of $35 for 1 year at 7 per cent? Ans. $2.45. 4. What is the interest of $42.05 for 1 year, at 4 at 44 per cent.? at 5 per cent.? at 54 per cent.? at 7 per cent. ? at 74 per cent.? at 81 per cent.?" at 9 per cent.? at 10 per cent.? at 10 per cent. ? at 11 per cent.?

Ans. to the last, $4.94.

5. What is the interest of $715 for 1 year, at 7 per cent.? Ans. $50.05 184. It is plain that the interest of any sum for 2 years, will be double the interest for 1 year; that for 3 years it will be 3 times the interest for 1 year, &c.

Hence, to find the interest of ANY SUM for ANY NUMBER of years, we

have this

RULE. Multiply the interest for ONE YEAR by the NUMBER OF

YEARS.

6. What is the interest of $100 at 6 per cent. for 1 year? years? for 3 years?

for 2

7. What is the interest of $85.624 for 5 years, at 6 per cent. ?

$85.625
.06

5.13750, interest for 1 year.

5, number of years.

Ans. $25.68750, interest for 5 years.

3. What is the interest of $125 for 3 years, at 7 per cent.?
9. Interest of $17.824 for 4 years, at 6 per cent.?
of $712.05 for 7 years, at 5
of $119.57 for 5 years, at 14 per cent.?
of $312.05 for 3 years at 7 per cent.?

10.

11. 12.

per cent.?

MONTHS AND DAYS.

185. The interest of $1 for 1 year, at 6 per cent., is

.06 cents; which is

.01 cent for 2 months,

Ans. $26.25. Ans. $4.81+. Ans. $249.213. Ans. $26.974. Ans. $65.53--...

.005 mills (or half a cent) for 1 month of 30 days; and
.001 mill for every 6 days.

From which it appears, that the interest of $1, at 6 per cent., will be half as many CENTS as there are months, and as many mills as there are days. Hence, if we take HALF THE MONTHS, AND OF THE DAYS, it will give the interest, in cents and mills, of $1 at 6 per cent., for ANY

GIVEN TIME.

13. What is the interest of $1 at 6 per cent., for 5mo. 20d.?

Half the months is 2; hence the interest for 5 months is 24 cents, or $.025. 1 of the days is 3; consequently the interest for 20 days is 33 mills, and the interest for the whole time, $.0284.

Or, we may add the odd month (= 30 days) to the 20, and take of the sum. Thus, we would have for 4 months 2 cents, for the odd month and days, (= 50d.,) 83 mills; and the whole would be $.0283, as before.

14. What is the interest of $1 at 6 per cent., for 7 months?

& 15 days?

for 10 months?

21d.

for 8 months?

for 10mo. 19d.?

for 6mo. 8mo. 27d. ? for 9 months? --for 11 months? for 11mo. Ans. to last, $.0584.

186. The interest of $2 is evidently twice as much as the interest of $1, the interest of $3 is 3 times as much, &c.

Hence, to find the interest of ANY SUM for ANY GIVEN TIME, at 6 per rent., we have this

RULE. Multiply the GIVEN SUM by half the even number of months, written as HUNDREDTHS, and ¦ of the number of days, written as THOUSANDTHS.*

15. What is the interest of $217, 624 at 6 per cent., for 14 years 9 months and 20 days?

Half the even number of months is 38, written as hundredths thus, .88; of the number of days (30+20) is 34, written as thousandths thus, .008}; the whole making .8884, for the multiplier.

$217.625

Hence

* When the days are less than 6, it is evident, we must put 0 in the place of mille.

16. What is the interest of $114 at 6 per cent. for 9mo. 14 days ?

17. Interest of $194 for 4mo. 12 days?

18.

19.

20.

21.

of $263.48 for 2mo. 21 days?
of $318 for 10mo. 16 days?
of $418 for 1Y. 7mo. 17 days?
of $268.44 for 3Y. 5mo. 26 days?

187. 7 per cent is 1 more than 6 per cent. Hence

To find the interest of any sum at 7 per cent.

Ans. $5.396
Ans. $4.268.

Ans. $3.556.

Ans. $16.748.

Ans. 940.894.

Ans. $56.193.

RULE. First find the interest at 6 per cent.; then add to it } part of itself.*

22. What is the interest of $165 for 2Y. 7mo. at 7 per cent.?

$165 principal.

.155 interest of $1 for the given time

.15 &

825

825

.155, the

165

[at 6 per cent.

$25.575 interest at 6 per cent.

+1=4.261

Ans. $29.836 interest at 7 per cent.

23. What is the interest of $519.20 for 3Y. 9mo. at 7 per cent? 24. Interest of $145 for 2Y. 3mo. ?

188. UNIVERSALLY when interest is at ANY OTHER rate than

6 PER CENT,

RULE. Find the interest at SIX PER CENT.; then add to it, or subtract from it, such part as the rate REQUIRED exceeds or falls short of 6 per cent.*

30. What is the interest of $45 for 10 months, at 44 per cent.?

of 6 per cent.; therefore, from the interest at 6 per cent we subtract of itself, and obtain the interest at 44 per cent.

31. Interest of $354 for 14 months at 5 per cent.?
of $501.21 for 5mo. 21d., at 4 per cent.?
of $721.09 for 11mo. 6d., at 8 per cent.?
of $999.99 for 1mo. 17d., at 10 per cent.?
of $95 for 21mo. 24d., at 121 per cent. ?
of $777.77 for 18d., at 15 per cent.?
37. What is the amount of $52 for 27mo., at 6 per cent.?
38. Amount of $101.72 for 9 mo. 12d., at 7 per cent. ?
of $514.51 for 17mo. 18d., at 8 per cent. ?

Ans. $20.65.

Ans. $9.523.

Ans. $53.841. Ans. $13.055.. Ans. $21.573. Ans. $5.833.

Ans. $59.02.

Ans. $107.297.
Ans. $574.879.

Or, find the interest for the even years, and take parts for the months and days.