Daboll's Schoolmaster's Assistant, Improved and Enlarged

47. Bought a pipe of wine for 84 dollars, and found ft had leaked out 12 gallons; I sold the remainder at 121 cents a pint; what did I gain or lose?

Ans. I gained $30. 48. A gentleman bought 18 pipes of wine at 12s. 6d. (New-Jersey currency) per gallon; how many dollars will pay the purchase? Ans. $3780. 49. Bought a quantity of plate, weighing 15 lb. 11 oz. 13 pwt. 17 gr. how many dollars will pay for it, at the rate of 12s. 7d. New-York currency, per ounce ?

Ans. $301, 50cts 2,8m.

50. A factor bought a certain quantity of broadcloth and drugget, which together cost 817. the quantity of broadcloth was 50 yards, at 18s. per yard, and for every 5 yards of broadcloth he had 9 yards of drugget; I demand how many yards of drugget he had, and what it cost him per yard? Ans. 90 yards at 8s. per yard. 51. IfI give 1 eagle, 2 dollars 8 dimes, 2 cents and 5 mills, for 675 tops, how many tops will 19 mills buy? Ans. 1 top 52. Whereas an eagle and a cent just three score yards

did buy, How many yards of that same cloth for 15 dimes had I ? Ans. Syds. Sqrs. Sna.+ 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 dollars, 75 cents on the list?

Ans. 82, 55cts. Smi 54. If 100 dollars gain 6 dollars interest in a year, how much will 49 dollars gain in the same time? Axs. 82. Girds

55. If 60 gallons of water, in one hour, fall inte a cus tern containing 300 gallons, and by a pipe in the chie 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 woad; but A goes 5 days before B. at the rate of 15 miles a day; B follows at the rate of 20 miles a day; what distance must he travel to overtake A ?

Ans. 300 miles.

RULE OF THREE INVERSE.

"ale of Three Inverse, teaches by having three

given to find a fourth, which shall have the same tion to the second, as the first has to the third. If more requires more, or less requires less, the ques tios 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:

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

men

days

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

men

days

onen

2. If 4 require 2 how much time will re. quire? Answer, 4 days. Here less requires more, viz. the less the number of men are, the more days are requir ed-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. SO men. days, when the will he perform Ans. 6 days.

2. If a man performs a journey in 5 day 12 hours long, in how many days it when the day is but 10 hours long P 3 What length of beard 74 inches wide, will make a equare foot ? Ans. 194 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.

loat

5. If when wheat is 7s. 6d. the bushel, the penny will weigh 9oz. what ought it to weigh when wheat is 6s. per bushel ? Ars. 11oz. 5pwt. 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 bushels. 7. If 100l. 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, what 15 men would be 20 days about? Ans. 60 men.

10. Suppose 650 men are in a garrison, and their provisions calculated to last but two months; how many men must leave the garrison that the same provisions may be sufficient for those who remain five months?

Ans. 390 men. 11. A regiment of soldiers consisting of 850 men are to be clothed, each suit to contain 34 yds. of cloth, which is 14 yards wide, and lined with shalloon yard wides how many yards of shalloon will complete the lining? Ans. 6941yds. 2qrs. 23na.

PRACTICE.

PRACTICE is a contraction of the Rule of Three Direct, when the first term happens to be an unit or one, and is a concise method of resolving mest 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 ma ny other writers have done.

Tables of Aliquot, or Even Parts.

Parts of a Shilling. Parts of a Pound. Parts of a cwt.

s. d.

The aliquot part of any number, is such a part of it, as being taken a certain number of times, exactly nakes that number.

CASE I.

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

Or find the value of the given quartity at 2s. per yard, &c. and divide said value by the even part which the given price is of £s. 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 4613 yards of tape come to, at 1¿d per yd.?

s. d.

1d. | | 461 6 value of 4614 yds. at 1s. per yd.

5,7 81

£2 178. 8d. value at 14d.

2. What cost 956lb. of cheese at 8d. per pound? Sd. | 3 | £25 12s. value of 256lb. at 2s. per lb.

£8 10s. 8. value of 8d. per pound

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

EXAMPLES.

What will 1294 yards cost at 2s. 6d. per yard?

s. d.

Yds.

£. s.