Problem of the Week

Updated at Mar 3, 2025 1:55 PM

This week's problem comes from the equation category.

How would you solve the equation \(\frac{10(2+m)}{3-m}=40\)?

Let's begin!



\[\frac{10(2+m)}{3-m}=40\]

1
Multiply both sides by \(3-m\).
\[10(2+m)=40(3-m)\]

2
Divide both sides by \(10\).
\[2+m=4(3-m)\]

3
Expand.
\[2+m=12-4m\]

4
Subtract \(2\) from both sides.
\[m=12-4m-2\]

5
Simplify  \(12-4m-2\)  to  \(-4m+10\).
\[m=-4m+10\]

6
Add \(4m\) to both sides.
\[m+4m=10\]

7
Simplify  \(m+4m\)  to  \(5m\).
\[5m=10\]

8
Divide both sides by \(5\).
\[m=\frac{10}{5}\]

9
Simplify  \(\frac{10}{5}\)  to  \(2\).
\[m=2\]

Done
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