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, $\frac{x}{10}$ is the amount of green marbles in $1$, and $\frac{x}{9}$ is the amount of green marbles in $2$. $\frac{x}{9}+\frac{x}{10}=\frac{19x}{90}$, $\frac{19x}{90}=95$, and $x=450$ marbles in each jar. Because the $\frac{9x}{10}$ is the amount of blue marbles in jar $1$, and $\frac{8x}{9}$ is the amount of blue marbles in jar $2$, $\frac{9x}{10}-\frac{8x}{9}=\frac{x}{90}$, so there must be $5$ more marbles in jar $1$ than jar $2$. The answer is $\boxed{A}$

 2019 AMC 10B (Problems • Answer Key • Resources) Preceded byProblem 10 Followed byProblem 12 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 10 Problems and Solutions

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