Question 10 • Advanced Algebra: Concepts and Connections
A carnival charges each person an admission fee and a fee per ride. A family pays 6 admission fees, and they pay for a total of 20 rides. A couple pays 2 admission fees, and they pay for a total of 18 rides. The family pays a total of 64 dollars The couple pays a total of 44 dollars Which augmented matrix can be used to determine the cost per admission and the cost per ride?
Answer
A
the 2 by 3 matrix row 1, 6 2 64 row 2, 20 18 44
B
the 2 by 3 matrix row 1, 6 20 44 row 2, 2 18 64
C
the 2 by 3 matrix row 1, 6 2 44 row 2, 20 18 64
D
the 2 by 3 matrix row 1, 6 20 64 row 2, 2 18 44
Explanation
Let x be the cost per admission and y the cost per ride. The family’s costs give 6x + 20y = 64, and the couple’s costs give 2x + 18y = 44. Putting each equation’s coefficients first and its total after the divider gives rows [6, 20, 64] and [2, 18, 44], which is choice D.
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