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2014 AMC 12A Problem 2

Problem 2 of 25EasierArithmetic

At the theater children get in for half price. The price for 55 adult tickets and 44 child tickets is $24.50.\$24.50. How much would 88 adult tickets and 66 child tickets cost?

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Solution

Since a child ticket is half an adult ticket, 55 adult and 44 child tickets equal 5+12⋅4=75+\tfrac12\cdot4=7 adult tickets, so one adult ticket costs 24.507=$3.50.\dfrac{24.50}{7}=\$3.50. The second purchase equals 8+12⋅6=118+\tfrac12\cdot6=11 adult tickets, costing 11⋅3.50=$38.50.11\cdot 3.50=\$38.50. Thus, the correct answer is B.
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