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36. A merchant bought 14 pipes of wine, and is allowed 6 months credit, but for ready njoney gets it 8 cts. a gallon cheaper; how much did he save by paying ready money?

Ans. $141, 12 cts. Examples promiscuously placed. 37. Sold a ship for 5371. and I owned of her; what was my part of the money?

Ans. £201 7s, 6d. 38. If of a ship cost 781 dollars 25 cents, what is the whole worth?

As 5 : 781,25 : : 16 : $2500 Ans. 39. If I buy 54 yards of cloth for 311. lus. what did it per Ell English ?

Ans. 14s. 7d. 40. Bought of Mr. Grocer, 11 cwt. 3 ąrs. of sugar, at 8 dollars 12 cents per cwt and gave him James Paywell's note for 191. 7s. (New-England currency) the rest I pay in cash ; tell me how many dols. will make up the balance ?

Ans. $30, 91 cts. 41. If a staff 5 feet long cast a shade on level ground 8 feet, what is the height of that steeple whose shade at the same time measures 181 feet?

Ans. 1131 ft. 42. If a gentleman have an income of 300 English guineas a year, how much nsay he spend, one day with another, tc lay up $500 at the year's end? Ans. $2,46 cts.5 m.

43. Bought 50 pieces of kerseys, each 34 Ells Flemish, at Ss. 4d. per Ell English; what did the whole cost? Ans. £425.

44. Bought 200 yards of cambrick for 901. but being damaged, I am willing to lose 71. 10s. by the sale of it; what must I demand per Ell English ? ARs. 10s. 3d.

45. How many pieces of Holland, each 20 Ells Flemish, inay i have for 231.8s. at 6s.6d. per Ell English? Ans. 6 pcs.

46. A merchant bought a bale of cloth containing 240 yds. at the rate of $7} for 5 yds. and sold it again at the rate of $11; for 7 yards; did he gain or lose by the bargain, and how much :

Ans. He gained $25, 71 ets. 4 m. + 47. Bought a pipe of wine for 84 dollars, and found it had leaked out 12 gals. ; I sold the remainder at 12; cts. a pint; what did I gain or lose ?

Ans. I gained $30. 48. A gentleman bought 18 pipes of wing at 12s. 6d. (New Jersey currency) per gallon; how many dollars will pay the purchase ?

Ans. $3780.

how many

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40. Bought a quantity of plate, weighing 15 lb. 11 oz. 13 pwt. 17 gr.

dols. will

pay for it, at the rate of 12s, 7d. New-York currency, per oz. ? Ans. $301, 50, cts. 2m.

50. A factor bought a certain quantity of broadcloth and drugget, which together cost 81l. the quantity of broadcloth was 50 yds., at 18s. per yd., and for every 5 yds. of broadcloth he had 9 yards of drugget; I demand how many yds. of drugget he had, and what it cost him per yard ?

Ans. 90 yds. at 8s. per yd. 51. If I give 1 eagle, 2 dols. 8 dimes, 2 cts. and 5 m. for 675 tops, how many tops will 19 mills buy?

Ans. 1 top. 52 Whereas an eagle and a cent just threescore yards

did buy, How many yards of that same cloth for 15 dimes had I ?

Ans. 8 yds. 3 qrs. 3 na. + 53. If the legislature of a state grant a tax of 8 mills on the dollar, how much must that man pay who is 319 dols. 75 cents on the list ?

Ans. $2, 55 cts. 8 m. 54. If 100 dols. gain 6 dols. interest in a year, how much will 49 dols. gain in the same tiine ? Ans. $2, 94 cts.

55. If 60 gallons of water, in one hour, fall into a cistern containing 300 gallons, and by a pipe in the cistern 35 gallons run out in an hour; in what time will it be filled ?

Ans. in 12 hours. 56. A and B depart from the same place and travel the same road; but A goes 5 days before B, at the rate of 15 miles a day; B follows at the rate of 20 mile a day; what distance must he travel to overtake A ? Ans. 300 miles.

RULE OF THREE INVERSE. THE Rule of Three Inverse, teaches by having three numbers given to find a fourth, which shall have the same proportion to the second, as the first has to the third:

If more requires more, or less requires less, the question belongs to the Rule of Three Direct.

But if more requires less, or less requires more, the question belongs to the Rule of Three Inverse; which may always be known from the nature and tenor of the question. For example:

1

men

men

men

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If 2 men can mow a field in 4 days, how many days will it require 4 men to mow it?

days 1. If 2 require 4 how much time will 4 require ? Answer, 2 days. Here more requires less, viz. the more men the less time is required.

days 2. If 4 require 2 how much time will 2 require ? Answer, 4 days. Here less requires more, viz. the less the number of men are, the more days are required therefore the question belongs to Inverse Proportion.

Rule.-1. State and reduce the terms as in the Rule of Three Direct.

2. Multiply the first and second terms together, and divide the product by the third ; the quotient will be the answer in the same denomination as the middle term was reduced into.

EXAMPLES.

1. If 12 men can build a wall in 20 days, how many men can do the same in 8 days?

Ans. 30 men. 2. If a man perform a journey in 5 days, when the day ís 12 hours long, in how many days will he perform it when the day is but 10 hours long?

Ans. 6 days. 3. What length of board 7 inches wide, will make a square foot ?

Ans. 191 inches. 4. If five dollars will pay for the carriage of 2 cwt. 150 miles, how far may 15 cwt be carried for the same money?

Ans. 20 miles. 5. If wben wheat is 78. 6d. the bushel, the penny loaf will weigh 9 oz. what ought it to weigh when wheat is 6s.

Ans. 11 oz. 5 put. 6. If 30 bushels of grain, at 50 cts. per bushel, will pay a debt, how many bushels at 75 cents per bushel,

will

pay the same?

Ans. 20 bushcls. 7. If 1001. in 12 months gain 61. interest, what principal will gain the same in 8 months ?

Ans, £150. 8. If 11 men can build a house in 5 months, by working 12 hours per day-in what time will the same number of men do it, when they work only 8 hours per day?

Ans. 7 months. 9. What number of men must be employed to finish in 5 days, wbat 15 men would be 20 days about? Ans. 60 men.

per bushel ?

10. Suppose 650 men are in a garrison, and their provie gions calculated to last but 2 months, how many men must leave the garrison that the same provisions may be sufficient for those who remain 5 months ? Ans. 390 men.

11. A regiment of soldiers consisting of 850 men are to be clothed, each suli to contain 3} yards of cloth, which is 14 yds. wide, and lined with shalloonyd. wide; how many yards of shalloon will complete the lining ?

Ans. 6941 yds. 2 qrs. 2 na.

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PRACTICE. PRACTICE is a contraction of the Rule of Three Direc., when the first term happens to be a unit or one, and is a concise method of resolving most questions that occur in trade or business where money is reckoned in pounds, shillings and pence; but reckoning in federal money will render this rule almost useless : for which reason I shall not enlarge so much on the subject as many other writers have done.

Tables of Aliquot, or Even Parts. Parts of a shilling. Parts of a pound.

Parts of a cwt, d.

£

16. cwt.
6 is
10 O is

56 is
4
6 8

28
3
5 0

16
2
4 0

14
1
3 4

7
Parts of 2 shillings. 2 6
ls. is

18 8d.

The aliquot part of any number is 6d.

such a part of it, as being taken a cere. 4d.

tain number of times, exactly makes 3d.

that number. 2d.

CASE I. When the price of one yard, pound, &c. is an even part of one shilling-Fmd the value of the given quantity at 1s. 1 yard, pound, &c. and divide it by that even part, and the quotient will be the answer in shillings, &c.

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Or find the value of the given quantity at 2s. per yd. &c. and divide said value by the even part which the given price is of 2s. and the quotient will be the answer in shillings, &c. which reduce to pounds.

N. B. To find the value of any quantity at 2s. you need only double the unit figure for shillings; the other figures will be pounds.

EXAMPLES.

1. What will 461; yds. of tape come to at l;d. per yd ?

d. 1 d. 1 1 461 6 value of 461 yds. at Is. per yd.

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5,7 87

S. d.

£2 17s. 8 d. value at 11d. 2. What cost 256 lb. of cheese at 8d. per pound? 8d. / } | £25 12s. value of 256 lb. at 2s. per lb.

£8 10s. 3d. value at 8d. per pound. Yards. per yard.

£. 486, at 1d.

Answers. 2 061
862 at 2d.

ny 38
911
at 3d.

11 79
749 at 4d.

12 98
113 at 6d.

2 16 6
899
at 8d.

29 19 4

CASE II. When the price is an even part of a pound-Find tho value of the given quantity at one pound per yard, &c. and divide it by that even part, and the quotient will be the an swer in pounds.

EXAMPLES.

8. d.

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What will 1297 yards cost at 2s.6d. per yard ?
£.

£.
2 6 + 129 10 value at 1 per yard.

Ans. £16 3s. 9d. value at 2s. 6d. Yds.

£. s. d. 123 at 10 O per yard Answers. 61 10 0 687} at 50

171 17 6

per yard.

s. d.

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