INVERSE PROPORTION.

RULE.

Transpose the inverse extremes; that is, set that of the first place under the third, and that in the third under the first; then work as in direct proportion. Note. See the note in direct proportion.

EXAMPLES.

1 If 7 men can reap 84 acres of wheat in 12 days; how many men can reap 100 acres in 5 days ?

If 84A.
xzd. S

5

420

7m.

S100A.

gd. Inverse term.

12

1200

7

420)84010(20m. answer.

84

00

Contracted.

If $4.4.2 m. (Xøø.4. (20 men.

8 1

{

2 If 4 dollars be the hire of 8 men for three days; how many days must 20 men work for 40 dols. answer 12 days, 3 If 4 men have 24 shillings for three days work, how many men will earn 41. 16s. in 10 days Panswer 3 men, 4 Suppose the interest of 3331. 6s. 8d. for 9 months be 151. what principal in 12 months will gain 61. P uns. 100% 5 If 200lb. be carried 40 miles for 40 cts.; how far may 20200lb. be carried for 60,60? answer 60 miles, 6 If 145 men can make a wall 32 feet high and 40 feet long in 8 days; in how many days can 68 men build a wall 28 feet high of the same length ? answer 14 days, 11h.

9. An usurer put out 861. to receive interest for the same; and when it had continued 8 months, he received for principal and interest 881. 17s. 4d. query the rate per cent ?

answer 5 per cent.

PRACTICE.

RACTICE is the short method of finding the value of any quantity of goods, by the given price of an integer. Note. See the rules in the several cases under this head.

PROOF.

Practice may be proved by varying the parts; by compound multiplication; or by the single rule of three direct.

When the price of an integer is less than a penny;

RULE.

Take such aliquot part or parts of the given quantity, as the price is of a penny, for the answer in pence; which reduce to pounds.

Note 1. When the complement of the given price, in any case, is an aliquot part, deduct the said aliquot part of the given quantity therefrom, and the remainder will be the answer, of the same denomination with the integer of which the divisor is à part.

2. When a remainder occurs in any example, either in this or the following cases, let it be reduced to the next lower denomination, &c.

EXAMPLES.

When the given price of an integer is a penny, or more, but less than a shilling;

Take such part or parts of the given quantity, as the price is of a shilling, for the answer in shillings.

EXAMPLES.

17612 yards, at Id. per yard, and at 11d.

7612

When the given price of an integer is more than one shilling, and less than two;

RULE.

Let the given quantity stand for so many shillings, to which add the amount in shillings of said quantity at the overplus price, found by case 1 or 2, for the answer in shillings.