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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,
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 ?
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.
1. State and reduce the terms as in die lure 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.
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 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 : ruare foot?
Ans. 194 inches
per bushel ?
4. If five dollars will pay for the carriage of 2 cwt. 150 miles, how far may 15 cwt. be carried for the same mo
Ans. 20 miles. 5. If when wheat is 7s. 6d. the bushel, the penny loaf will weigh 9oz. what ought it to weigh when wheat is 6s.
Ans. 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 1001. in 12 months gain 61. interest, what principal will gain the same in 8 months ? Ans £150.
8. If il 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 to 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 31 yds. of cloth, which is 17 yards wide, and lined with shalloon yard wide ; how many yards of shalloon will complete the lining?
Ans. 6941yds. 2qrs. 2nd.
PRACTICE. PRACTICE is a contraction of the Rule of Three Direct, 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 wilí render this rule almost useless : for which reason I shall not enlarge so much on the subject as many other writer's have done.
Tables of Aliquot, or Even Parts. l'arts of a Shilling. Parts of a Pound. | Parts of a cwt. d. s. d. £.
The aliquot part of any number 4d.
is such a part of it, as being taken a 3d.
certain number of times, exactly 2d.
makes 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 quantity at 2s. per yard, &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.
1. What will 4611 yards of tape come to, at id per yd
d. 1 d. 461 6 value of 461; yds. at 1s. per yd.
£2 178. 8 d. value at 1 d. 2. What cost 256lb. of cheese at 8d. per pound? 8d. 1 | £25 12s. value of 256lb. at 2s. per lb.
58 10s. 8d. value at 8d. per pound.
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.
What will 129? yards cost at 2s. 6d. per yard ?
Ans, £16 39. 9d. value at 2s.' 6d. per yard.
£. $. d.
Answers. 61 10 0
171 17 6 2113 at 4 0
42 5 0 543 at 6 8
181 0 0 127 at 3 4
3 4 461 at 18
38 8 4
Note. When the price is pounds only, the given quantity multiplied thereby, will be the answer. EXAMPLES.--11 tins of hay at 4l. per tan. Thus 11
When the given price is any number of shillings un der 20.
i When the shillings are an even number, 'multiply
the quantity by half the number of shillings, and double the first figure of the product for shillings ; and the rest of the product will be pounds.
2. If the shillings be odd, multiply the quantity by the whole number of shillings, and the product will be the answer in shillings, which reduce to pounds.
1st. 124 yds. at 8s.
2d. 132 yds. at 7s. per yd.
£49 12s. Ains
l'da 562 at 4s. 378 at 2s. 213 at 14s.
CASE IV. When the given price is pence, or pence and farthings, and not an even part of a shilling--Find the value of the given quantity at 1s. per yard, &c. which divide by the greatest even part of a shilling contained in the given price, and take parts of the quotient for the remainder of the price, and the sum of these several quotients will be the answer in shillings, &c. which reduce to pounds.
What will 245 lb. of raisins come to, at 9 d. per lb ?
0 value of 245 lb. at 1s. per pound.
Ans. £9 19 0} value of the whole at 9 d. per lb.