Paul made two types of pie: strawberry and blueberry. He cut all of the strawberry pies into 10 slices each and all of the blueberry pies into 9 slices each. If Paul cut the same total number of slices of each type of pie, what is the minimum number of slices of each type he could have cut?
Question
Paul made two types of pie: strawberry and blueberry. He cut all of the strawberry pies into 10 slices each and all of the blueberry pies into 9 slices each. If Paul cut the same total number of slices of each type of pie, what is the minimum number of slices of each type he could have cut?
Solution
Paul could have cut a minimum of 90 slices for each type of pie. Here's how:
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Since Paul cut the strawberry pies into 10 slices each, the total number of strawberry pie slices must be a multiple of 10.
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Similarly, since he cut the blueberry pies into 9 slices each, the total number of blueberry pie slices must be a multiple of 9.
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To find the smallest number that is a multiple of both 10 and 9, we need to find the least common multiple (LCM) of 10 and 9.
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The LCM of 10 and 9 is 90.
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Therefore, the minimum number of slices Paul could have cut for each type of pie is 90.
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