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 $7.84 \%$ acid.
A) No solution
B) $27 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 23 \mathrm {~cm} ^ { 3 }$ of $10 \%$
C) $3.92 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 46.08 \mathrm {~cm} ^ { 3 }$ of $10 \%$
D) $50 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 50 \mathrm {~cm} ^ { 3 }$ of $10 \%$

Question

Quizplus · Accepted Answer

To solve this problem, we can set up a system of linear equations and then represent it in matrix form. Let $x$ be the volume of the 6% solution and $y$ be the volume of the 10% solution. We have two conditions:1. The total volume should be 50 cm³: $x + y = 50$.2. The total concentration should be 7.84% of the final solution: $0.06x + 0.10y = 0.0784 \times 50$.Solving this system of equations, we find that $x = 27$ cm³ and $y = 23$ cm³.

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

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