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2019 AMC 10B Problem 11

Problem 11 of 25IntermediateAlgebra

Two jars each contain the same number of marbles, and every marble is either blue or green. In Jar 11 the ratio of blue to green marbles is 9:1,9:1, and the ratio of blue to green marbles in Jar 22 is 8:1.8:1. There are 9595 green marbles in all. How many more blue marbles are in Jar 11 than in Jar 2?2?

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Solution

Let xx and yy be the numbers of green marbles in Jars 11 and 22, respectively. Then the total numbers of marbles in the jars are 10x10x and 9y9y. The jars contain the same number of marbles, so 10x=9y10x=9y. Also x+y=95x+y=95. Solving gives x=45x=45 and y=50y=50. Jar 11 has 9x=4059x=405 blue marbles, and Jar 22 has 8y=4008y=400 blue marbles. The difference is 55. Thus, A is the correct answer.

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Concepts: ratio and proportion · system of equations

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.