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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 ticket price and c be the child ticket price. The two purchases give two equations: 3a + 2c = 37 and 5a + 4c = 69.
Double the first equation so its c-term matches the second: 2 × (3a + 2c) = 2 × 37, so 6a + 4c = 74. Subtract the second equation from this result: (6a + 4c) − (5a + 4c) = 74 − 69, so a = 5.
Substitute a = 5 into 3a + 2c = 37: 3(5) + 2c = 37, so 15 + 2c = 37, then 2c = 22 and c = 11. Check both original equations: 3(5) + 2(11) = 15 + 22 = 37, and 5(5) + 4(11) = 25 + 44 = 69.
One child ticket costs $11.
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