7. A certain man lent out £36 to receive interest for the same, and when it had continued 8 months he received for principal and interest together, the sum of £33 17s. 4d. I demand at what per cent. per annum he received interest?

Answer £5 per cent. per annum.

8. I demand the interest of 250 dollars for 73 days, at 6 dollars per cent. per annum?

D.

D. 250 × 73 6

Answer $3

9. If 200lbs. be carried 40 miles for 50 cents, what sum will pay for the carriage of 20200lbs. 60 miles?

Ans. $75.75 cents. 10. If 180 bushels of oats be sufficient for 18 horses 20 days, how many bushels will serve 60 horses 36 days? Ans. 1080 bush. 11. If a regiment of 936 soldiers eat 312 quarters of wheat in 84 days, how many quarters will suffice an army of 11088 soldiers 56 days? Ans. 2164 quarters. 12. I demand the interest of 2240 dollars for 7 years, at $6 per cent. per annum. Ans. $940.80 cents. 13. If a wagoner charge 7 dollars for the wagonage of 700 lbs. 120 miles, how much must I pay him for the wagonage of 4200lbs. 240 miles?

Ans. $84. 14. What is the interest of 669 dollars for 3 years and 9 months, at $5 per cent. per annum? Ans. $125.43 cents. 15. If a family of 12 persons use 6 barrels of flour in 3 months, how many barrels will they use in a year if 6 more be taken into the family? Ans. 36 barrels. 16. If a man borrowed $1070 on interest, and at the expiration of 18 months have to pay $1262.60cts., at what rate per cent. per annum, was the interest computed? Ans. $12 per cent.

17. If 8 reapers received £3 4s. for 4 days' work, what sum will pay 48 reapers for 16 days' work?

Ans. £76 16s.

18. If a family of 9 people expend $450 in 5 months, how much will be sufficient to maintain them 8 months, if 5 people more come into the family? Ans. $1120. 19. What is the interest of 654 dollars for 164 days, at $6 per cent. per annum? Ans. $17.63cts.+41 rem.

20. A certain usurer put out $250 to receive interest for the same, and when it had continued 9 months, he received for principal and interest the sum of $261.25cts. At what rate per cent. per annum, was the interest calculated? Ans. 6 per cent.

21. What is the interest of $947 for 294 days, at $6 per cent. per annum ? Ans. $15.76cts. 7m+125 rem. 22. I demand the interest on $1333.33 cts. for 1 week, at $6 per cent. per annum? Ans. $1.53cts. 8m.+72. 23. If 7 men use 98lbs. of flour in 14 days, how many barrels will be sufficient for 28 men 56 days?

Ans. 8 barrels. 24. A man and his wife, having wrought 3 days, received $2.25 cts. in payment; how much must they have for 10 days, when their two sons help them?

Ans. $15.

THE DOUBLE RULE OF THREE INVERSE.

The Double Rule of Three Inverse is a compound of Direct and Inverse Proportion, and is composed of five terms, which are given in the question to find the answer-three of them are called the terms of supposition, and the other two the terms of demand.

A RULE FOR STATING THE QUESTIONS, &C.

1. Set the term of supposition in the first place, that is of the like name with the answer required to the question.

2. Set the term of supposition in the second place, that signifies the time in which the gain is acquired, the loss sustained, or the work, &c. performed.

3. If the answer to the question be required in days, &c.-then, set the days in the first place, and their length (if given) in the second. See the 5th question.

4. The agents that perform the work or the commodity to be removed, &c. may occupy the second place in the statings.*

5. Set the term of supposition in the third place, that designates the gain or loss, the work performed, the distance travelled, the wages earned, or the price paid for the removal of any commodity, &c. 6. Set the two terms of demand in a line with the three terms of supposition, so that the second and fourth terms of the stating may be of one name; also, the third and fifth, and the stating will be completed.

* Examine the third and sixth questions carefully.

7. Multiply the third and fourth terms together for a divisor and the three remaining ones for a dividend the quotient thence arising will be the answer required, and of like name with the first term in the stating, or whatever it was reduced to.

8. The questions may be proved by reversing the order of the stating and working backward, which will produce the first term of the first stating, if the work in both be right.

9. Questions may be answered by two single statings, one of which will be direct proportion and the other inverse, and the answer to the first stating will always be the middle term of the second one.

10. Whenever a dividing term can be divided by a multiplying term, or a multiplying term by a dividing term, the operation may be abbreviated by using the quotients thence arising, instead of the whole

terms.

EXAMPLES.

1. If 7 men can reap 84 acres of wheat in men can reap 100 acres in 5 days? M. D.

1 2 M. D. A. D.

5

A.

If 7x12: 84×5 :: 100

12 days, how many
A.
A.

If 20×5:

100 × 12 :: 84

5

See the work abbreviated.

As 7x12: 84×5 :: 100

Ans. 20 men.

Ans. 500£

9x3-27 days, Ans.

OF DIRECT AND INVERSE PROPORTION.

A RULE TO FIND WHETHER THE PROPORTION IS DIRECT OR INVERSE. 1. Let the principal cause of gain or loss, interest or demand, inGrease or decrease, &c. oecupy the first place in the stating.

2. Let the term which signifies the time or the distance of one place from another, occupy the second place in the stating.

3. Let the term which denotes the gain or loss, the action performed, or the price paid for removing any commodity, occupy the third place in the stating.

4. Place the two terms of demand under those of the same name in the supposition, and a blank place will occur under that term, which is of like name with the answer.

5. If the blank should fall under the third term, the proportion is direct-therefore multiply the first and second terms together for a divisor, and the other three for a dividend.

6. If the blank should fall under the first or second term, the proportion is inverse-therefore multiply the third and fourth terms together for a divisor, and the other three for a dividend; and the quotient, in either case, will be the answer required.

NOTE 1. In the 1st example, the blank place will occur under 100 acres, which is the the third term; therefore the proportion is direct ; consequently, move the 7 men and 12 days into the 4th and 5th places of the stating, and proceed by direct proportion to find the

answer.

NOTE 2. In the 2d example, the blank place will occur under 36 days, which is the 2d term; therefore, the proportion is inverse ; consequently, move the 18 horses and 180 bushels into the 4th and 5th places of the stating, and proceed by inverse proportion to find the answer.

PROMISCUOUS EXAMPLES.

1. If 20 men mow 100 acres of grass in 5 days, how many acres can 7 men mow in 12 days? Ans. 84 acres. 2. If 60 horses can eat 1080 bushels of oats in 36 days, in how many days will 18 horses eat 180 bushels ? Ans. 20 days. 3. If 500 dollars principal gain 20 dollars interest in 8 months, at what rate per cent. per annum was the interest computed? Ans. at $6 per cent. per annum. 4. If 60 horses can eat 1080 bushels of oats in 36 days, how many horses will eat 180 bushels in 20 days? Ans. 18 horses. 5. If 32 men earn 338 dollars in 24 days, in what time will 16 men earn $56.33 cents? Ans. 8 days. 6. If I pay 84 dollars for the carriage of 4200lbs. 240 miles, how far may 700lbs. be carried for 7 dollars? Ans. 120 miles. 7. What sum will gain $33.75 cents in 9 months, at 6 dollars per cent. per annum? Ans. 750 dollars.

8. A wall which is to be built 27 feet high has been raised 9 feet in 6 days by 12 men; how many men must be employed to finish the work in 4 days? Ans, 36 men. 20 days, how many Ans. 1350 pair.

9. If 5 men can make 150 pair of shoes in pair can 15 men make in 60 days?