Solve the problem using matrices.
-A chemist has prepared two acid solutions, one of which is $4 \%$ acid by volume, another $11 \%$ acid. How many cubic centimeters of each should the chemist mix together to obtain $50 \mathrm {~cm} ^ { 3 }$ of a solution that is $6.24 \%$ acid.
A) No solution
B) $20 \mathrm {~cm} ^ { 3 }$ of $4 \% ; 20 \mathrm {~cm} ^ { 3 }$ of $11 \%$
C) $34 \mathrm {~cm} ^ { 3 }$ of $4 \% ; 16 \mathrm {~cm} ^ { 3 }$ of $11 \%$
D) $3.12 \mathrm {~cm} ^ { 3 }$ of $4 \% ; 46.88 \mathrm {~cm} ^ { 3 }$ of $11 \%$

Question

Quizplus · Accepted Answer

To solve this problem, we can set up a system of linear equations and represent it in matrix form. Let $x$ be the volume of the 4% solution and $y$ be the volume of the 11% solution. We have two equations:1. $x + y = 50$ (The total volume of the mixture is 50 cm³)2. $0.04x + 0.11y = 0.0624 \times 50$ (The total volume of acid in the mixture)Solving this system of equations, we find $x = 34$ and $y = 16$, meaning 34 cm³ of the 4% solution and 16 cm³ of the 11% solution are needed.

Solve the Problem Using Matrices 4%4 \%4% Acid by Volume, Another 11%11 \%11%

Solve the Problem Using Matrices $4 \%$ Acid by Volume, Another $11 \%$