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2015 AMC 10A Problem 4

Problem 4 of 25EasierArithmetic

Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as many eggs as Sofia, and Sofia had twice as many eggs as Mia. Pablo decides to give some of his eggs to Sofia and Mia so that all three will have the same number of eggs. What fraction of his eggs should Pablo give to Sofia?

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Solution

Let mm be the number of candy eggs that Mia had. Then Sofia had 2m2m eggs and Pablo had 6m6m eggs. The total number of eggs is then m+2m+6m=9m. m + 2m + 6m = 9m. For all of them to have the same number of eggs, they each must have 9m÷3=3m9m \div 3 = 3m eggs. Sofia needs 3m−2m=m3m - 2m = m more eggs. This means Pablo must give m6m=16\dfrac{m}{6m} = \dfrac{1}{6} of his eggs to Sofia. Thus, B is the correct answer.
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