Problem:
Big Al, the ape, ate bananas from May through May . Each day he ate six more bananas than on the previous day. How many bananas did Big Al eat on May
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Solution:
You can solve this problem by guessing and checking. If Big Al had eaten bananas on May , then he would have eaten bananas. This is bananas too many, so he actually ate fewer bananas each day. Thus, Big Al ate bananas on May and bananas on May .
The average number of bananas eaten per day was . Because the number of bananas eaten on consecutive days differs by and there are an odd number of days, the average is also the median. Therefore, the average number of bananas he ate per day, , is equal to the number of bananas he ate on May . So on May Big Al ate bananas.
Let be the number of bananas that Big Al ate on May . The following chart documents his banana intake for the five days.
The total number of bananas Big Al ate was , which must be . So Big Al ate bananas on May .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions