2019 AMC 10B Problems/Problem 11

Problem

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?

$\textbf{(A) } 5\qquad\textbf{(B) } 10 \qquad\textbf{(C) }25 \qquad\textbf{(D) } 45 \qquad \textbf{(E) } 50$

Solution

Call the amount of marbles in each jar $x$ , because they are equivalent. Thus, $x/10$ is the amount of green marbles in $1$ , and $x/9$ is the amount of green marbles in $2$ . $x/9+x/10=19x/90$ , $19x/90=95$ , and $x=450$ marbles in each jar. Because the $9/10$ is the amount of blue marbles in jar $1$ , and $8/9$ is the amount of blue marbles in jar $2$ , $9x/10-8x/9=x/90$ , so there must be $5$ more marbles in jar $1$ than jar $2$ . The answer is $A$

(Edited by Lcz)

2019 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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2019 AMC 10B Problems/Problem 11

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