A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 110 ounces of a mixture that is 80% salt. How many ounces of each solution should she use?

Answer 1

Let x be the number of ounces of Solution A and y be the number of ounces of Solution B.

We have the following two equations:

1. x + y = 110 (total amount of mixture)
2. 0.65x + 0.90y = 0.80(110) (salt content)

Solving the first equation for x, we get x = 110 - y.

Substitute x into the second equation:

0.65(110 - y) + 0.90y = 0.80(110)
71.5 - 0.65y + 0.90y = 88
0.25y = 16.5
y = 66

Substitute y back into x = 110 - y:

x = 110 - 66
x = 44

Therefore, the scientist should use 44 ounces of Solution A and 66 ounces of Solution B to obtain 110 ounces of a mixture that is 80% salt.