Problem of the Week

Updated at Jan 18, 2021 9:03 AM

This week we have another equation problem:

How can we solve the equation 4+4×52+n=2234+4\times \frac{5}{2+n}=\frac{22}{3}?

Let's start!



4+4×52+n=2234+4\times \frac{5}{2+n}=\frac{22}{3}

1
Simplify  4×52+n4\times \frac{5}{2+n}  to  202+n\frac{20}{2+n}.
4+202+n=2234+\frac{20}{2+n}=\frac{22}{3}

2
Subtract 44 from both sides.
202+n=223−4\frac{20}{2+n}=\frac{22}{3}-4

3
Simplify  223−4\frac{22}{3}-4  to  103\frac{10}{3}.
202+n=103\frac{20}{2+n}=\frac{10}{3}

4
Multiply both sides by 2+n2+n.
20=103(2+n)20=\frac{10}{3}(2+n)

5
Simplify  103(2+n)\frac{10}{3}(2+n)  to  10(2+n)3\frac{10(2+n)}{3}.
20=10(2+n)320=\frac{10(2+n)}{3}

6
Multiply both sides by 33.
20×3=10(2+n)20\times 3=10(2+n)

7
Simplify  20×320\times 3  to  6060.
60=10(2+n)60=10(2+n)

8
Divide both sides by 1010.
6010=2+n\frac{60}{10}=2+n

9
Simplify  6010\frac{60}{10}  to  66.
6=2+n6=2+n

10
Subtract 22 from both sides.
6−2=n6-2=n

11
Simplify  6−26-2  to  44.
4=n4=n

12
Switch sides.
n=4n=4

Done
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