Difference between revisions of "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 $2$. $\frac{x}{9}+\frac{x}{10}=\frac{19x}{90}$, $\frac{19x}{90}=95$, 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 $(\boxed{A})$

(Edited by Lcz)