AnswersAdvanced Algebra Concepts and ConnectionsModeling with Matrices — QuizQuestion 17
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Modeling with Matrices — Quiz

Question 17 • Advanced Algebra: Concepts and Connections

A chemist has a container of 12 percent peroxide solution and a container of 20 percent peroxide solution. She needs to mix the two solutions to create 100 mL of a 14 percent solution. If x represents the amount of 12 percent peroxide solution and y represents the amount of 20 percent peroxide solution she needs, which matrix equation can determine the amount of each solution she needs to make the 14 percent solution?

Answer
A
the 2 by 2 matrix row 1, 0 point 1 2 0 point 2 row 2, 1 1 the 2 by 1 column matrix x y is equal to the 2 by 1 column matrix 0 point 1 4 100
B
the 2 by 2 matrix row 1, 1 1 row 2, 0 point 1 2 0 point 2 the 2 by 1 column matrix x y is equal to the 2 by 1 column matrix 0 point 1 4 100
C
the 2 by 2 matrix row 1, 1 1 row 2, 0 point 1 2 0 point 2 the 2 by 1 column matrix x y is equal to the 2 by 1 column matrix 14 100
D
the 2 by 2 matrix row 1, 0 point 1 2 0 point 2 row 2, 1 1 the 2 by 1 column matrix x y is equal to the 2 by 1 column matrix 14 100

Explanation

The total-volume equation is x + y = 100. The amount of pure peroxide in the mixture must be 14 mL, since 14% of 100 mL is 14 mL, so 0.12x + 0.20y = 14. Putting the concentration equation first and the volume equation second gives choice D: the rows [0.12, 0.20] and [1, 1] with right-hand side [14, 100].

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