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In the town of Arkville, a total of 80 people came in to be tested for Lyme disease. Half of them were found to have the disease. Of those who did not have the disease when first tested, one quarter later developed it. What fraction of the original 80 people got Lyme disease?

Explanation

Half of the 80 people tested originally had Lyme disease—that’s 40 people. Of the other 40 people, one quarter later developed Lyme disease. One-quarter of 40 is 10. So a total of 50 got Lyme disease out of 80 people, \(\frac{50}{80}=\frac{5}{8}\)

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