2010 AMC 10A Problem 3

Below is the professionally curated solution for Problem 3 of the 2010 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2010 AMC 10A solutions, or check the answer key.

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Concepts:linear equation ratio and proportion

Difficulty rating: 960

Tyrone had $97$ marbles and Eric had $11$ 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?

$3$

$13$

$18$

$25$

$29$

Solution:

Let $x$ be the number of marbles that Eric ends up with. Then Tyrone ends up with $2x.$

The total number of marbles is $97 + 11 = 108,$ so $3x = 108$ $x = 36.$

Then, Tyrone ends up with $36 \cdot 2 = 72$ marbles. This means he has to give away $97 - 72 = 25$ marbles.

Thus, D is the correct answer.

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