Marbles are to be removed from a jar that contains $24$ red marbles and $24$ black marbles. What is the least number of marbles that could be removed so that the ratio of the red marbles to the black marbles left in the jar will be $6$ to $5$

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[STEP]Setup the equation of ratio of red marbles to black marbles left in the jar[/STEP]

Suppose we have to remove $x$ black marbles. Then the ratio red marbles and the black marbles left in the jar will be

\begin{eqnarray*}
\frac{24}{24-x} & = & \frac{6}{5}\\
24\times5 & = & 6\left(24-x\right)\\
120 & = & 144-6x\\
6x & = & 144-120\\
x & = & \frac{24}{6}\\
& = & 4
\end{eqnarray*}

[ANS]Hence at least we have to remove $4$ marbles.[/ANS]

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