Chemicals A & B are formed by mixing x, y & z in the ratio of 8:3:4 and 4:3:8 respectively.?

Question

Chemicals A & B are formed by mixing x, y & z in the ratio of 8:3:4 and 4:3:8 respectively.? the cost per liter of x, y and z is $300, $240 and $180 respectively. Chemical C is produced by mixing chemicals A & B in a certain ratio. If Total Cost of producing 1000 liters of chemical C is $252000 find the ratio of Chemicals A & B in Chemical C.

Answer 1

1 Liter of A = 8/15*X+3/15*Y+4/15*Z

1 liter of B = 4/15 * X + 3/15*Y + 8/15*Z

Cost of 1 liter of A = 8/15*$300 + 3/15*$240 + 4/15 *$180 = $256 / Liter

Cost of 1 liter of B = 4/15*$300 + 3/15*$240 + 8/15*$180 = $224 / Liter

Cost of 1 liter of C = $252,000/$1,000 = $252

Cost of 1 liter of C = $256*A/(A+B) + $224*B/(A+B)

$252 = $256*A/(A+B) + $224*B/(A+B)

252A + 252B = 256*A + 224*B

28 B = 4 A

7 B = A

The ratio of A to B in Chemical C is 7 to 1.