Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. Which equation can Bruce use to determine how much of the 10% alcohol solution he should use?

A. 0.10x + 0.15 (50 - x) = 50 + 0.12

B. 0.10x + 0.15 (50 - x) = 0.12 (50)

C. 0.10x + 0.15 (50 - x) = 50 + 0.12 + 0.12 (50)

D. (0.10x) (0.15) (50 - x) = 0.12 (50)

Question

Dalia Patrick

Mathematics

27 September, 09:35

Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. Which equation can Bruce use to determine how much of the 10% alcohol solution he should use?

A. 0.10x + 0.15 (50 - x) = 50 + 0.12

B. 0.10x + 0.15 (50 - x) = 0.12 (50)

C. 0.10x + 0.15 (50 - x) = 50 + 0.12 + 0.12 (50)

D. (0.10x) (0.15) (50 - x) = 0.12 (50)

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Answers (1)

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Potter · Answer 1

B

Here, x is the volume of the 10ml solution. Multiplying it by its concentration gives the amount of alcohol in it. 50 is the total volume of the 12% solution so (50 - x) gives the volume of the 15% solution. Multiplying this by the concentration gives the amount of alcohol in it. The sum of these amounts of alcohols is equivalent to the amount of alcohol in the 12% solution which is given by the product of its volume and concentration.