Question

A hardware store mixes paints in a ratio of two parts blue to six parts red to make two gallons of cabbage red. A ration of five parts blue to three parts red makes two gallons of eggplant purple. A gallon of cabbage red sells for $24, and a gallon of eggplant purple sells for $21. Find the cost of 1 quart of blue paint and the cost of 1 quart of red paint.

One quart of blue paint costs $
One quart of red paint costs $

Answer 1

2 b + 6 r = 2 * 24

5 b + 3 r = 2 * 21 ... 10 b + 6 r = 84

subtracting equations (to eliminate r) ... 8 b = 36

solve for b , then substitute back to find r

Answer 2

23 4