2019 AMC 10B Problems/Problem 11

Revision as of 20:10, 14 February 2019 by Mathlover66 (talk | contribs) (Solution)

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)

See Also

2019 AMC 10B (ProblemsAnswer KeyResources)
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

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