Question

solving mixture problems
quiz complete
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?
○ 0.15(40) + 0.6x = 0.25(40 + x)
○ 0.15(40) + 0.6(x − 40) = 0.25(x)
○ 0.15(40) + 0.6x = 0.25(40 − x)
○ 0.15(40) + 0.6(x + 40) = 0.25(x)

Explanation:

Step1: Analyze paint A's black pigment

Paint A is 40 ml, 15% black. So black from A: $0.15\times40$.

Step2: Analyze paint B's black pigment

Total mixture is $x$ ml, so paint B is $x - 40$ ml (since A is 40 ml). Paint B is 60% black, so black from B: $0.6\times(x - 40)$.

Step3: Analyze mixture's black pigment

Mixture is $x$ ml, 25% black. So black in mixture: $0.25\times x$.

Step4: Set up the equation

Black from A + Black from B = Black in mixture. So $0.15(40) + 0.6(x - 40) = 0.25(x)$.

Answer:

B. $0.15(40) + 0.6(x - 40) = 0.25(x)$