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The ratio between the numbers of pens and pencils in the supply room is $3:4$. Lucy takes $5$ pens away, and now the ratio between the numbers of pens and pencils becomes $2:3$. How many pencils are there in the supply room?

 Oct 21, 2020
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Say the number of pencils is \(x\) and the number of pens is \(y.\)

We get, 

\(\begin{align*} \frac{y}{x} = \frac{3}{4} \\ \frac{y-5}{x} = \frac{2}{3} \\ 4y = 3x \\ 3y-15 = 2x \\ x = 60 \\ y = 45 \end{align*}\)

 

Therefore, the number of pencils is 60. (the equation is reasonably easy to solve with substiuation. 

 Oct 21, 2020

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