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 by Problem 10	Followed by Problem 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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

2019 AMC 10B Problems/Problem 11

Problem

Solution

See Also