Solve using a system of two equations in two unknowns.
-A chemist needs 100 milliliters of a 70% solution but has only 66% and 86% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.
A) 90 milliliters of 66%; 30 milliliters of 86%
B) 90 milliliters of 66%; 20 milliliters of 86%
C) 80 milliliters of 66%; 20 milliliters of 86%
D) 20 milliliters of 66%; 80 milliliters of 86%

Question

Quizplus · Accepted Answer

Let x be the amount of the 66% solution and y be the amount of the 86% solution. We can set up the following system of equations:
x + y = 100 (since the chemist needs 100 milliliters of the final solution)
0.66x + 0.86y = 0.7(100) (since the final solution must be 70%)
Solving this system of equations gives x = 80 and y = 20, so the chemist needs 80 milliliters of the 66% solution and 20 milliliters of the 86% solution. Therefore, the answer is choice C.

Solve Using a System of Two Equations in Two Unknowns