Need
a hardware store mixes paints in a ratio of three parts blue to five parts yellow to make two gallons of lime green. a ratio of six parts blue to two parts yellow makes two gallons of ocean blue. a gallon of lime green sells for $29, and a gallon of ocean blue sells for $32. find the cost of 1 quart of blue paint and the cost of 1 quart of yellow paint.

Step-by-step explanation:

Each of the 2-gallon mixes is made of 8 "parts" of paint, so each "part" is 2/8 gallons = 1/4 gallon = 1 quart. We can let b and y represent the costs of 1 quart of blue and yellow paint, respectively.

Then the cost for 2 gallons is ...

  3b + 5y = 58 . . . lime green

  6b +2y = 64 . . . ocean blue

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Subtracting the second equation from twice the first gives ...

  2(3b +5y) -(6b +2y) = 2(58) -(64)

  8y = 52

  y = 6.5

From the first equation, ...

  3b = 58 -5y = 58 -5·6.5 = 25.5

  b = 25.5/3 = 8.5

The cost of 1 quart of blue paint is $8.50; the cost of 1 quart of yellow paint is $6.50.