AMC 10

Ratio and Proportion , 2019 AMC 10B Problem 11

The simplest example of ratio and proportion is based upon finding number of marbles in two jars having two different color marbles . Learn in this self-learning module for math olympiad

Ratio and Proportion

The given problem is based upon calculating the number of marbles in jars of specific color, to do so we have to use ratios of the marbles of different colors and use the ratio to calculate the actual number of marbles of required color.

Try the 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 $2$?

$\textbf{(A) } 5\qquad\textbf{(B) } 10 \qquad\textbf{(C) }25 \qquad\textbf{(D) } 45 \qquad \textbf{(E) } 50$

2019 AMC 10B Problem 11

Ratio and proportion

6 out of 10

Secrets in Inequalities.

Knowledge Graph

Ratio problem- knowledge graph

Use some hints

Let \(2x\) is the total no of marbles in both the jars. so each of the jar have \(x\) marbles.

Thus, $\frac{x}{10}$ is the number of green marbles in Jar $1$, and $\frac{x}{9}$ is the number of green marbles in Jar $2$.

Since $\frac{x}{9}+\frac{x}{10}=\frac{19x}{90}$, we have $\frac{19x}{90}=95$, so there are $x=450$ marbles in each jar.

Since \(\frac{9}{10}th\) of the jar 1 marbles are of blue color and \(\frac{8}{9}th\) of the jar 2 marbles are of blue color.

Now we can easily find the no of blue marbles in both the jars and then we can subtract them to get the amount by which one exceed the other.

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