\fdO'^ - Old Forge Coal Mines

134 ALGEBRA.
(c)
9x' - 12x = 21.
Dividing by 9, x* ~- — ,
Completing the square,
Extracting square root,
3 "^\3/ 3 "^9" 9*
2 5
x — — = ± -.
o o
2 5 7
Transposing, ;ir = - + - = -,
2 5 3
^" ^=3-3=-3=-^-
7
Therefore, ;r = — , or — 1. Ans.
o
(253) {c-i)-i = c\ Ans. (Art. 526, HI.)
(;«|/«')-i = w-*(«l)-J = w-J«-* = — j-j.
Ans.
{cd'')i = c^d'a, or V^d^\ or y ~. Ans. (Art. 530.)
(254)
Let X = number of quarts of 90-cent wine in the mixture.
y = number of quarts of 50-cent wine in the mixture
Then, x+}'=60, (1)
and 90;r + 50y = 4,500 = 75 X 60. (2)
Multiplying (1) by 50,
50^ +50j/= 3,000. (3)
Subtracting (3) from (2),
40^=1,500;
whence, x = 37— qt. Ans.
Multiplying (1) by 90, 90-r + 90j = 5,400 (4)
Subtracting (2), 90.r+50j = 4,500 (2)
40j= 900;
whence, j = 22^ qt. Ans.