Problem:
A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted children and wheels. How many tricycles were there?
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Answer Choices:
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Solution:
The following chart shows that the answer must be tricycles.
Let equal the number of bicycles and equal the number of tricycles. Then the number of vehicles is , and the number of wheels is . Because , it follows that
If each child had a bicycle, there would be wheels. Since there are wheels, of the vehicles must be tricycles.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions