Problem of the Week

Updated at Apr 20, 2020 1:46 PM

For this week we've brought you this equation problem.

How would you solve the equation \(\frac{10(3-n)}{2+n}=\frac{20}{3}\)?

Here are the steps:



\[\frac{10(3-n)}{2+n}=\frac{20}{3}\]

1
Multiply both sides by \(2+n\).
\[10(3-n)=\frac{20}{3}(2+n)\]

2
Simplify  \(\frac{20}{3}(2+n)\)  to  \(\frac{20(2+n)}{3}\).
\[10(3-n)=\frac{20(2+n)}{3}\]

3
Multiply both sides by \(3\).
\[30(3-n)=20(2+n)\]

4
Expand.
\[90-30n=40+20n\]

5
Add \(30n\) to both sides.
\[90=40+20n+30n\]

6
Simplify  \(40+20n+30n\)  to  \(40+50n\).
\[90=40+50n\]

7
Subtract \(40\) from both sides.
\[90-40=50n\]

8
Simplify  \(90-40\)  to  \(50\).
\[50=50n\]

9
Divide both sides by \(50\).
\[1=n\]

10
Switch sides.
\[n=1\]

Done
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