Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 60% salt and Solution B is 85% salt. She wants to obtain 30 ounces of a mixture that is 80% salt. How many ounces of each solution should she use?

Answer 1

Let x be the amount (in ounces) of solution A and y the amount of solution B that the scientist uses. She wants a new solution with a total volume of 30 ounces, so that

x + y = 30

Each ounce of solution A contributes 0.6 oz of salt, and each ounce of solution B contributes 0.85 oz of salt. The new solution needs to have 80% of 30 oz of salt, or 24 oz, so that

0.6x + 0.85y = 24

x + y = 30 ==> y = 30 - x

0.6x + 0.85(30 - x) = 24 ==> 0.6x + 25.5 - 0.85x = 24 ==> 0.25x = 1.5 ==> x = 1/6 (about 0.167)

y = 30 - 1/6 ==> y = 179/6 (or about 29.83)