Difference between revisions of "2019 AMC 10B Problems/Problem 11"

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==Problem==
 
==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?
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Two jars each contain the same number of marbles, and every marble is either blue or green. In Jar <math>1</math> the ratio of blue to green marbles is <math>9:1</math>, and the ratio of blue to green marbles in Jar <math>2</math> is <math>8:1</math>. There are <math>95</math> green marbles in all. How many more blue marbles are in Jar <math>1</math> than in Jar <math>2</math>?
  
 
<math>\textbf{(A) } 5\qquad\textbf{(B) } 10 \qquad\textbf{(C) }25  \qquad\textbf{(D) } 45  \qquad \textbf{(E) } 50</math>
 
<math>\textbf{(A) } 5\qquad\textbf{(B) } 10 \qquad\textbf{(C) }25  \qquad\textbf{(D) } 45  \qquad \textbf{(E) } 50</math>

Revision as of 19:57, 17 February 2019

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 $\boxed{A}$

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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