Problem:
Every week Roger pays for a movie ticket and a soda out of his allowance. Last week, Roger's allowance was dollars. The cost of his movie ticket was of the difference between and the cost of his soda, while the cost of his soda was of the difference between and the cost of his movie ticket. To the nearest whole percent, what fraction of did Roger pay for his movie ticket and soda?
Answer Choices:
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Solution:
Let be the cost of Roger's movie ticket, and let be the cost of Roger's soda. Then and . Thus and . Solving the system for and in terms of gives and . The total cost of the movie ticket and soda as a fraction of is .
The problems on this page are the property of the MAA's American Mathematics Competitions