14
QuizMultiple Choice

Adding and Subtracting Matrices — Cumulative exam

Question 14 • GA-Advanced Algebra: Concepts and Connections CR

A cleaning solution is made from vinegar, lemon juice, and water. The table below shows the part of the total solution that is in each element. Solution Components Solution ASolution BSolution CVinegar0.10.20.4Lemon Juice0.150.20.1Water0.750.60.5Mr. Allen needs 100 mL of a solution that is 30% vinegar, 15% lemon juice, and 55% water. How much of solution A will Mr. Allen need to make his cleaning solution?

Answer
A
0 mL
B
10 mL
C
30 mL
D
50 mL

Explanation

Let A, B, and C be the fractions of the 100 mL batch made from each solution. The target percentages require 0.10A + 0.20B + 0.40C = 0.30 and 0.15A + 0.20B + 0.10C = 0.15, with A + B + C = 1. Solving these equations gives A = 0, so Mr. Allen needs 0 mL of solution A. In fact, equal amounts of B and C give 30% vinegar and 15% lemon juice.

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