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 \(\frac{5}{2+y}+\frac{20}{y}=\frac{23}{3}\)?

Check out the solution below!



\[\frac{5}{2+y}+\frac{20}{y}=\frac{23}{3}\]

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

2
Simplify.
\[75y+120=46y+23{y}^{2}\]

3
Move all terms to one side.
\[75y+120-46y-23{y}^{2}=0\]

4
Simplify  \(75y+120-46y-23{y}^{2}\)  to  \(29y+120-23{y}^{2}\).
\[29y+120-23{y}^{2}=0\]

5
Multiply both sides by \(-1\).
\[23{y}^{2}-29y-120=0\]

6
Split the second term in \(23{y}^{2}-29y-120\) into two terms.
\[23{y}^{2}+40y-69y-120=0\]

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

8
Factor out the common term \(23y+40\).
\[(23y+40)(y-3)=0\]

9
Solve for \(y\).
\[y=-\frac{40}{23},3\]

Done

Decimal Form: -1.739130, 3
Cymath foriOSAndroid