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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.

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 $2$?

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

Source

Competency

Difficulty

Suggested Book

2019 AMC 10B Problem 11

Ratio and proportion

6 out of 10

Secrets in Inequalities.

First hint

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.

Second Hint

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.

Final Step

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.

- https://www.cheenta.com/consecutive-terms-of-a-series-b-stat-hons-2003-problem-1/
- https://www.youtube.com/watch?v=ST58GTF95t4

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