Problem of the Week

Updated at Jun 13, 2022 4:09 PM

To get more practice in equation, we brought you this problem of the week:

How can we solve the equation 52+y+20y=233\frac{5}{2+y}+\frac{20}{y}=\frac{23}{3}?

Check out the solution below!



52+y+20y=233\frac{5}{2+y}+\frac{20}{y}=\frac{23}{3}

1
Multiply both sides by the Least Common Denominator: 3y(2+y)3y(2+y).
15y+60(2+y)=23y(2+y)15y+60(2+y)=23y(2+y)

2
Simplify.
75y+120=46y+23y275y+120=46y+23{y}^{2}

3
Move all terms to one side.
75y+120−46y−23y2=075y+120-46y-23{y}^{2}=0

4
Simplify  75y+120−46y−23y275y+120-46y-23{y}^{2}  to  29y+120−23y229y+120-23{y}^{2}.
29y+120−23y2=029y+120-23{y}^{2}=0

5
Multiply both sides by −1-1.
23y2−29y−120=023{y}^{2}-29y-120=0

6
Split the second term in 23y2−29y−12023{y}^{2}-29y-120 into two terms.
23y2+40y−69y−120=023{y}^{2}+40y-69y-120=0

7
Factor out common terms in the first two terms, then in the last two terms.
y(23y+40)−3(23y+40)=0y(23y+40)-3(23y+40)=0

8
Factor out the common term 23y+4023y+40.
(23y+40)(y−3)=0(23y+40)(y-3)=0

9
Solve for yy.
y=−4023,3y=-\frac{40}{23},3

Done

Decimal Form: -1.739130, 3
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