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2010 AMC 10A Problem 3

Problem 3 of 25EasierAlgebraArithmetic

Tyrone had 9797 marbles and Eric had 1111 marbles. Tyrone then gave some of his marbles to Eric so that Tyrone ended with twice as many marbles as Eric. How many marbles did Tyrone give to Eric?

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Solution

Let xx be the number of marbles that Eric ends up with. Then Tyrone ends up with 2x.2x. The total number of marbles is 97+11=108,97 + 11 = 108, so 3x=108 3x = 108 x=36.x = 36. Then, Tyrone ends up with 36⋅2=7236 \cdot 2 = 72 marbles. This means he has to give away 97−72=2597 - 72 = 25 marbles. Thus, D is the correct answer.
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