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3. If 150 dolls. in 8 months gain 6 dolls. interest, in what time will 100 dolls. gain the same ?
150 :8:: 100
8 iloo) 12100
dolls, in what
12 months, Ans. 4. If 100 dolls. in 12 months gai in time will 150 dolls. gain the same ?
100 : 12 : : 150
15|0)12010(8 months, Ans.
120 5. If 7 men can do a piece of work in 10 days, how many men can do the same in 5 days ? Ans. 14.
6. If 14 men can do a piece of work in 5 days ; how many men can do the same in 10 days ? Ans. 7.
7. If a man perform a journey in 15 days, when the days were 12 hours long, how long ought the days to be, to travel the same distance in 12 days ? Ans.15 hours.
8. If a man perform a journey in 12 days, when the days were 15 hours long, another man travelling at the same rate, is 15 days going the same distance, how long were the days when the second man travelled ?
Ans. 12 hours. 9. A farmer hired a man for a year, was to give him a coat worth 15 dolls. and 120 dolls. but disagreeing, they parted ; the farmer gave him besides the coat, $ 52,50, how long did he tarry ? Ans. 6 months.
10. A man hasa garment making, which takes 2 yards of cloth of 11 yard wide ; as he wishes it to be lined with shalloon of of a yard wide, how much will complete the lining?
Ans. 4 yards. 11. If 48 men can build a wall in 24 days, how many men can do the same in 192 days ? Ans. 6 men.
12. If I lend my friend 100 dolls. for 6 months, (allowing 30 days to a month) how long ought he to lend me 1000 dols. to requite my kindness? Ans. 18 days.
13. How many yards of matting, that is half a yard wide, will cover a room that is 30 feet long, and 18 wide ?
Ans. 120 yds. L
14. How much in length, that is 3 inches wide, will make a square foot ?
Ans, 4 feet.
THE RULE OF PROPORTION;
Or, THE RULE OF THREE, STATED BY A METHOD WHICH
RENDERS ALL DISTINCTIONS OF DIRECT, INVERSE, SINGLE, OR DOUBLE PROPORTION, UNNECESSARY.
Case I. When three numbers or terms only are given.
RULE. Write down that number or term which is of the same kind or quality, the answer is to be, for the middle term, and reduce it to its lowest denomination.
2. Consider whether by the nature of the question, the answer must be more than the middle term, if so set down the greater of the other two numbers at the right of the middle term, and the less at the left ; but if the answer must be less than the middle term, set the less number at the right, and the greater at the left.
3. Multiply the middle and right hand terms into each other for a dividend, which divide by the left hand term, the quotient will be the answer in the same denomination the middle term was reduced to, which may (if need be) be reduced to its proper terms,
Note. If any or all the terms be of several denomina, tions, they must be reduced as in the Rule of Three Direct, &C.
Questions, in this rule may be proved by varying their order.
EXAMPLES 1. If 28s. will pay for the carriage of 1 cwt. 150 miles, how far can 6cwt. be carried for the same money?
6 : 150 :: 1
Ans. 25 miles.
2. There is a cistern having a cock which will empty it in 12 hours, how many such cocks will empty it in 15 minutes ?
15 : 1 :: 720
MISCELLANEOUS QUESTIONS, which, according to most authors, would some be called direct, and some inverse Proportion, but may all be solved by this last method.
1. If 120 men can do a piece of work in 8 months, how many men can do the same in 2 months ?
2 : 120 : : 8
480 Ans. 2. If 25 dolls. worth of wine will serve 46 men, when wine is 120 dolls. per tun, how many men will the same 25 dolls. worth servė, then the wine is 80 dolls. per tun ?
80 : 46 :: 120
Ans. 69 men.
3. At 15s. 11d. per cwt. what will 5 fother cost!
19 2 in a fother.
$77 11 10 Ans. NOTE. This 3d example would be by former authors in general called Direct Proportion.
4. How many yards of shalloon, that is of a yard wide, will line 9 yards of wide ? Ans. 21 yards.
5. If £652 13 4 is taxed £83 12 4, how much must 44 be taxed ?
Ans. 10s. 2d. Iqr. 19888 6. Two travellers set out from the same place, and at the same time, one travels East, 24 miles a day, the other West, 30 miles a day, till they were 2150 miles from each other, how long did they travel, allowing 12 hours to a day?
Ans. 39d. Oh. 46m. 40s. 7. At 10 cents a dozen, how many gross for $62,40 ?
Ans. 52 gross. 8. At 378 dolls. per tun, how many gallons of wine for $37,50 ?
Ans. 25 gallons. 9. Įf 7 times 6 barrels of flour cost 4 times 63 dolls. how much will 9 tiines 23 barrels cost ? Ans. 1242 dols.
10. A merchant bought 8000 barrels of flour for 27000 dolls. but by accident 1000 barrels were damaged, so as to be wholly lost ; how must he sell the remain. der per barrel, to gain 1000 dolls. ? Ans. 4 dolls.
il. If 12 dozen lb. 3 score lb. and 16 lb. of coffee cost 11 times 5 dolls. how much will 5 dozen lb. 7 times 9lb. and i1lb. cost?
Ans. $33,50. 12. Admit within atherial space,
A harmless dove to soar,
Admit that when the chase began,
And thaimsuch was the eagle's force,
Did just accomplish with ado :
Ans. 2666147 rods. Case II. When more than three numbers, or terms are given, as five, seven, nine, &c. which is generally called Compound or Double Rule of Three.
RULÉ. Select the middle term as in 'Case I.
2. Take two terms of like qualities, and dispose of them as directed in that Case,
3. Take two other terms of like qualities, and dispose of them in like manner, and so on till all the terms are disposed of, and reduced as directed.
4. Multiply the middle, term into all those at the right of it, the last product will be a dividend.
5. . Multiply all the terms at the left of the middle one together, for a divisor.
6. Divide the dividend by the divisor, the quotient will be the answer, as in Case I.
Noqe. Questions of this kind may be proved by vary.; ing their order. See first and second examples.
EXAMPLES 1. If 7 men in 12 days, can reap 84 acres, how many men in 5 days can reap 100 acres?