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At a community theater, the cost of 3 adult tickets and 2 child tickets is $37, and the cost of 5 adult tickets and 4 child tickets is $69. What is the cost, in dollars, of one child ticket?
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Correct answer
D
Let a be the adult price and c the child price. Then 3a + 2c = 37 and 5a + 4c = 69. Double the first equation: 6a + 4c = 74. Subtract the second: (6a + 4c) − (5a + 4c) = 74 − 69, so a = 5.
Substitute into 3a + 2c = 37: 15 + 2c = 37, so 2c = 22 and c = 11. Check: 5(5) + 4(11) = 25 + 44 = 69.
The child ticket costs $11. The trap (A) $5 is the adult price; the question asks for the child price.
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