Page:Elementary algebra (1896).djvu/84

66 Rh Whence the symbolical statement of the question is 3x- 100 = 200-8(60-x); 3x- 100 = 200 - 480 + 8 x, 480 - 100 - 200 = 8x - 3x, 5x= 180; x = 36, the greater part, and 60 — x = 24, the less.

Ex. 3. Divide 847 between A, B, C, so that A may have $10 more than B, and B $8 more than C.

Suppose that C has x dollars ; then B has x + 8 dollars, and A has x + 8 + 10 dollars. Hence x + (x+ 8) + (x + 8 + 10) = 47 ; x+ x+ 8 + x + 8 + 10 = 47, 3x = 21; x=7, so that C has $7, B $15, A $25.

Ex. 4. A person spent $112.80 in buying geese and ducks ; if each goose cost 14 dimes, and each duck 6 dimes, and if the total number of birds bought was 108, how many of each did he buy ?

In questions of this kind it is of essential importance to have all quantities expressed in the same denomination ; in the present instance it will be convenient to express the money in dimes.

Let x represent the number of geese, then 108 — x represents the number of ducks.

Since each goose cost 14 dimes, x geese cost 14 x dimes.

And since each duck cost 6 dimes, 108 — x ducks cost 6(108 — x), dimes.

Therefore the amount spent is 14x+ 6(108 -x) dimes; but the question states that the amount is. also $112.80, that is, 1128 dimes.

Hence 14x + 6(108 - x)= 1128 ; dividing by 2, 7 x + 324 - 3 x = 564, 4x= 240; x= 60, the number of geese ; and 108 — x = 48, the number of ducks.