Problem:
A class collects to buy flowers for a classmate who is in the hospital. Roses each, and carnations cost each. No other flowers are to be used. How many different bouquets could be purchased for exactly ?
Answer Choices:
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Solution:
The total cost of the carnations must be an even number of dollars. The total number of dollars spent is the even number , so the number of roses purchased must also be even. In addition, the number of roses purchased cannot exceed . Therefore the number of roses purchased must be one of the even integers between and , inclusive. This gives possibilities for the number of roses purchased, and consequently possibilities for the number of bouquets.
The problems on this page are the property of the MAA's American Mathematics Competitions