Solve the problem using matrices.
-A chemist has prepared two acid solutions, one of which is $6 \%$ acid by volume, another $10 \%$ acid. How many cubic centimeters of each should the chemist mix together to obtain $50 \mathrm {~cm} ^ { 3 }$ of a solution that is $8.24 \%$ acid.
A) No solution
B) $4.12 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 45.88 \mathrm {~cm} ^ { 3 }$ of $10 \%$
C) $50 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 50 \mathrm {~cm} ^ { 3 }$ of $10 \%$
D) $22 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 28 \mathrm {~cm} ^ { 3 }$ of $10 \%$

Question

Quizplus · Accepted Answer

To solve, set up the equations: $0.06x + 0.10y = 0.0824 \times 50$ and $x + y = 50$. Solving these gives $x = 22$ and $y = 28$.

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Solve the Problem Using Matrices $6 \%$ Acid by Volume, Another $10 \%$