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47. Bought a pipe of wine far. 84 dollars, and found it had leaked out 12 gallons; I sold the remainder at 12} cents a pint; what did I gäin or lose ?
Ans. I gained ss0. 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 02, 13 pwt. 17 gr. how many dollars will pay for it, at the rate of 12s. 7d. New-York currency, per ounce ?
Ans. 8301, 50cts. 2.. 30. A factor bought a certain quantity of broadcloth and drugget, which together cost 811. 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. If I give 1 eagle, 2 dollars, 8 dimes, 2 cents and 5 mills, for 675 tops, how many tops wiki 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. 3qrs. 3na. + 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. 8m. :54. If 100. dollars gain 6 dollars interest in a year, how much will 49 dollars gain in the same time?
Ans. 82, 94cts. 55. If 60 gallons of water, in one hour, fall into a cis. tern containing 300 gallons, and by a pipe in the cistern, 85 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 miles a day; what distauce ruust be travel to overtake A ?
Ans. 300 miler.
RULE OF THREE INVERSE. THE Rule of Thrce Inversé, teaches by having threenumbers given to find a fourth, which shall have the saine proportion to the second, as the first has to the third.
If more requires more, or less requires less, the ques. tion belongs to the Rule of Three Direct:
But if more l'equires 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 nen can mow a field in 4 days, how many days will it require 4 men to mow it? . .men days .. !
men : 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 in ...
men 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 requircd-therefore the question belongs to Inverse Proportion.
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 ; te quotient will be the answer in the same denomination as the middle terin was reduced into.
EXAMPLES. 1. If 1€ men can build a wall in 20 days, how many men can do the same in 8 days ? ins. 50 men."
2. If a man performs a journey in 5 days, when the day is 12 hours long, in how many days will be perform it when the day is but 10 hours long? Ans. 6 days.
3. What length of board 74 inches wide, will make a square 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. 5. If when wheat is 7s.6d. the bushel, the penny loaf will weigh 902. what ought it to weigh when wheat is 6s. per bushel ?
Ans. 11oz. 5pwt. 6. If so hushels of grain, at 50 cts. per bushel, will pay a dedi, how many bushels at 75 cents per bushel, will pay the same?
Ans. 20 bushels. 7. If 1001. in 12 months gain 61. interest, what principal will gain the same in 8 inonths ? Ans. £150.
8. If 11 men oan build a house in 5 months, by worki ing 12 hours per day--III 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 pro, visions 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 St yds. of cloth, which
is 14 yards wide, and lined with shalloon yard wide; fare kow many yards of shalloon will complete the lining?
Ans. 6941yds. 2qrs. 2 na.
PRACTICE is a contraction of the Rule of Three Direct, wben the first term happens to be an 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 mata ny other writers have done.
Tables of Aliquot, or Eren Parts. Parts of a Shilling.Parts of a Pound: Parts of a ché.
lbi cut. 6 is 100 is
56 is 68
28 = 1 . 3
Parts of 2 Shillings.
18. is of
The aliquot part of any number
lis such a part of it, as being taken a 3d.
certain number of times, exactly 2d.
makes that number.
CASE E. 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 quantity at 2s. per yarı, &c. and divide said value y 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. Iu find the value of any cuantity at 2s. you need only double the unit figure for shillings; the other fig. üres will be pounds.
EXAMPLES 1. What will 4611 yards of tape come to, at 1}d per yd.?
S. d. 13d. 1 | 461 6 value of 4611 yds. at 1s. per ye.
and divide it by that even part, and the quotient will be the answer in pounds.
What will 1294 yards cost at 2s. 6d. per yard ?
S. d. f.. S....
Ans. £16 Ss. 9d. valae at 2s. 6d. per yard.
tis. d. 323 at 10.0 per yard. 3. Answers. 61 10 0 687 at 5 0 immagini
E. 171 17 6. 2114 at 40 per
.:4250 ; 543 at 16 8
.-181 00 127 at 3.4 metros
. .., 2134 461 at 18 go
38 84 Note. When the price is pounds only, the given quant ity multiplied thereby, will be the answer.
EXAMPLE.--11 tons of nay at 4l. per ton. Thus 11
1. When the shillings are an even number, multiply