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 10(2+m)3−m=40\frac{10(2+m)}{3-m}=40?

Let's begin!



10(2+m)3−m=40\frac{10(2+m)}{3-m}=40

1
Multiply both sides by 3−m3-m.
10(2+m)=40(3−m)10(2+m)=40(3-m)

2
Divide both sides by 1010.
2+m=4(3−m)2+m=4(3-m)

3
Expand.
2+m=12−4m2+m=12-4m

4
Subtract 22 from both sides.
m=12−4m−2m=12-4m-2

5
Simplify  12−4m−212-4m-2  to  −4m+10-4m+10.
m=−4m+10m=-4m+10

6
Add 4m4m to both sides.
m+4m=10m+4m=10

7
Simplify  m+4mm+4m  to  5m5m.
5m=105m=10

8
Divide both sides by 55.
m=105m=\frac{10}{5}

9
Simplify  105\frac{10}{5}  to  22.
m=2m=2

Done
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