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 5 $$50 \mathrm {~cm} ^ { 3 }$$ of a solution
That is 6.66% acid.

A) $31 \mathrm {~cm} ^ { 3 }$ of $4 \% ; 19 \mathrm {~cm} ^ { 3 }$ of $11 \%$
B) $3.33 \mathrm {~cm} ^ { 3 }$ of $4 \% ; 46.67 \mathrm {~cm} ^ { 3 }$ of $11 \%$
C) $20 \mathrm {~cm} ^ { 3 }$ of $4 \% ; 20 \mathrm {~cm} ^ { 3 }$ of $11 \%$
D) No solution

Question

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 5 $$50 \mathrm {~cm} ^ { 3 }$$ of a solution
That is 6.66% acid.

A) $31 \mathrm {~cm} ^ { 3 }$ of $4 \% ; 19 \mathrm {~cm} ^ { 3 }$ of $11 \%$
B) $3.33 \mathrm {~cm} ^ { 3 }$ of $4 \% ; 46.67 \mathrm {~cm} ^ { 3 }$ of $11 \%$
C) $20 \mathrm {~cm} ^ { 3 }$ of $4 \% ; 20 \mathrm {~cm} ^ { 3 }$ of $11 \%$
D) No solution

Quizplus · Accepted Answer

To solve this, set up equations based on the total volume and the total amount of acid. Let $x$ be the volume of the 4% solution and $y$ be the volume of the 11% solution. The equations are:1. $x + y = 50$ (total volume)2. $0.04x + 0.11y = 0.0666 \times 50$ (total acid)Solving this system of equations yields $x = 31$ and $y = 19$, meaning $31 \mathrm {~cm} ^ { 3 }$ of the 4% solution and $19 \mathrm {~cm} ^ { 3 }$ of the 11% solution are needed.

Solve the Problem Using Matrices 50 cm350 \mathrm {~cm} ^ { 3 }50 cm3

Solve the Problem Using Matrices $50 \mathrm {~cm} ^ { 3 }$