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

question 432

Multiple Choice

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 \(10 \%\)

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Definitions:

Production Possibilities Frontier

A curve depicting all maximum output possibilities for two or more goods given a set of inputs.

Outward Shift

A movement of the supply or demand curve in an economic diagram indicating an increase in supply or demand, leading to changes in price and quantity.

Consumption Level

The total amount of goods and services that an individual or group consumes over a specific period.

Technological Improvement

Innovations and advancements in technology that enhance productivity, efficiency, and quality of goods and services.