Question

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 $2?$

$5$

$10$

$25$

$45$

$50$

Solution:

Let $x$ and $y$ be the numbers of green marbles in Jars $1$ and $2$ , respectively. Then the total numbers of marbles in the jars are $10x$ and $9y$ .

The jars contain the same number of marbles, so $10x=9y$ . Also $x+y=95$ . Solving gives $x=45$ and $y=50$ .

Jar $1$ has $9x=405$ blue marbles, and Jar $2$ has $8y=400$ blue marbles. The difference is $5$ . Thus, A is the correct answer.

2019 AMC 10B Problem 11

Solution:

Problem 11 in Other Years