Problem:
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 be the number of eggs that Mia has. Then Sofia has eggs and Pablo has eggs. If the total of eggs is to be divided equally, each person will have eggs. Therefore Pablo should give eggs to Mia and eggs to Sofia. The fraction of his eggs he should give to Sofia is .
The problems on this page are the property of the MAA's American Mathematics Competitions