Linear equations

Question

A scientist has two solutions, which she has labeled solution A and solution B. Each contains salt. She knows that solution A is 30% salt and solution B is 80% salt. She wants to obtain 50 ounces of a mixture that is 40% salt. How many ounces of each solution should she use?

Answer 1

Focus on the amt of salt in each solution.

For A oz. of sol'n A, the salt content is 0.30A

For B oz. of sol'n B, the salt content is 0.80B

We also know that A + B must = 50 oz. and the resulting solution is 40% salt.

So 0.30A + 0.80B = 0.40(50)

Since A = 50 - B we can substitute: 0.30 (50 - B) + 0.80B = 20

15 - 0.30B + 0.80B = 20 → 0.5B = 5 → B = 10 oz., then A = 40 oz.

Check: 0.8(10) + 0.3(40) = 8 + 12 = 20 oz of salt in 50 oz of solution. 20/50 = 40%