2019 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 11 Easy

Two jars each contain the same number of marbles, and every marble is either blue or green. In Jar 1 the ratio of blue to green marbles is 9:1, and the ratio of blue to green marbles in Jar 2 is 8:1. There are 95 green marbles in all. How many more blue marbles are in Jar 1 than in Jar 2? (2019 AMC 10B Problem, Question#11)

  • A.

    5

  • B.

    10

  • C.

    25

  • D.

    45

  • E.

    50

Answer:A

Call the number of marbles in each jar x (because the problem specifies that they each contain the same number). Thus, \frac {x}{10} is the number of green marbles in Jar 1, and \frac{x}{9} is the number of green marbles in Jar 2. Since \frac {x}{9}+\frac {x}{10}=\frac {19x}{90}, we have  \frac{19x}{90}=95, so there are x=450 marbles in each jar.

Because\frac{9x}{10} is the number of blue marbles in Jar 1, and \frac{8x}{9} is the number of blue marbles in Jar 2, tere are \frac{9x}{10}- \frac{8x}{9}= \frac{x}{90}=5 more mables in Jar 1 than Jar 2. This means the answers is \text {(A)} 5.

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