Surface Area of Tile Fragments

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At an archeological ruins site, flat tile fragments are discovered that have a collective surface area of 298 square feet. If the area of each fragment is at least 15 square feet, what is the greatest number of fragments that could be present in the discovery?

Review: Surface Area of Tile Fragments


Explanation

In this question, we want to know the greatest number of fragments possible. The greatest number of fragments means the smallest fragments, so we can have more of them. If we had 20 fragments each of the minimum size, the total would be square feet. That is 2 square feet too many. So we can take away one fragment and we have 19. If they are all the minimum size, then that covers square feet. But there isn't an upper limit on the sizes, so we could have 18 minimum-size fragments and one big fragment to cover the difference. So 20 is too many, while 19 is possible. Therefore, 19 is the maximum.

The correct answer is (C).


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