4
QuizMultiple Choice

Modeling with Matrices — Quiz

Question 4 • Advanced Algebra: Concepts and Connections

Indira has 18 coins valued at 4 point 2 0 dollars She has only quarters and dimes. Which augmented matrix can be used to determine the number of quarters and dimes in the collection?

Answer
A
the 2 by 3 matrix row 1, 1 0 point 2 5 4 point 2 0 row 2, 1 0 point 1 0 18
B
the 2 by 3 matrix row 1, 1 1 18 row 2, 0 point 2 5 0 point 1 0 4 point 2 0
C
the 2 by 3 matrix row 1, 1 0 point 2 5 18 row 2, 1 0 point 1 0 4 point 2 0
D
the 2 by 3 matrix row 1, 1 1 4 point 2 0 row 2, 0 point 2 5 0 point 1 0 18

Explanation

Let q be the number of quarters and d the number of dimes. The total number of coins gives q + d = 18, and their total value gives 0.25q + 0.10d = 4.20. The augmented matrix must place the coefficients and right-hand sides in matching rows: [1, 1 | 18] and [0.25, 0.10 | 4.20], which is choice B.

AI-written and checked against the verified answer.

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