Fifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 mL of paint color A, resulting in a paint that contains 25% black pigment. Which equation can be used to solve for x , the total amount of paint in the mixture of the two colors?
Answer
A
0 point 1 5 repeating 40 plus 0 point 6 x is equal to 0 point 2 5 times open paren 40 minus x close paren
B
0 point 1 5 repeating 40 plus 0 point 6 times open paren x plus 40 close paren is equal to 0 point 2 5 times x
C
0 point 1 5 repeating 40 plus 0 point 6 times open paren x minus 40 close paren is equal to 0 point 2 5 times x
D
0 point 1 5 repeating 40 plus 0 point 6 x is equal to 0 point 2 5 times open paren 40 plus x close paren
Explanation
The mixture has a total of x mL, including the 40 mL of paint A, so it contains x − 40 mL of paint B. The amount of black pigment is 0.15(40) from paint A plus 0.60(x − 40) from paint B, and the finished mixture has 0.25x mL of black pigment. Setting these equal gives 0.15(40) + 0.60(x − 40) = 0.25x, which is choice C.
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