Problem of the Week

Updated at May 6, 2019 4:09 PM

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

How can we solve the equation \(\frac{3}{3-w}+\frac{20}{w}=\frac{5}{2}\)?

Check out the solution below!



\[\frac{3}{3-w}+\frac{20}{w}=\frac{5}{2}\]

1
Multiply both sides by the Least Common Denominator: \(2w(3-w)\).
\[6w+40(3-w)=5w(3-w)\]

2
Simplify.
\[-34w+120=15w-5{w}^{2}\]

3
Move all terms to one side.
\[34w-120+15w-5{w}^{2}=0\]

4
Simplify  \(34w-120+15w-5{w}^{2}\)  to  \(49w-120-5{w}^{2}\).
\[49w-120-5{w}^{2}=0\]

5
Multiply both sides by \(-1\).
\[5{w}^{2}-49w+120=0\]

6
How?
Split the second term in \(5{w}^{2}-49w+120\) into two terms.
\[5{w}^{2}-24w-25w+120=0\]

7
Factor out common terms in the first two terms, then in the last two terms.
\[w(5w-24)-5(5w-24)=0\]

8
Factor out the common term \(5w-24\).
\[(5w-24)(w-5)=0\]

9
How?
Solve for \(w\).
\[w=\frac{24}{5},5\]

Done

Decimal Form: 4.8, 5