Problem of the Week

Updated at Jun 24, 2019 1:16 PM

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

How would you solve the equation \((5+\frac{5}{w})\times \frac{2}{2+w}=\frac{12}{7}\)?

Here are the steps:



\[(5+\frac{5}{w})\times \frac{2}{2+w}=\frac{12}{7}\]

1
Expand.
\[\frac{10}{2+w}+\frac{10}{w(2+w)}=\frac{12}{7}\]

2
Multiply both sides by the Least Common Denominator: \(7w(2+w)\).
\[70w+70=12w(2+w)\]

3
Simplify.
\[70w+70=24w+12{w}^{2}\]

4
Move all terms to one side.
\[70w+70-24w-12{w}^{2}=0\]

5
Simplify \(70w+70-24w-12{w}^{2}\) to \(46w+70-12{w}^{2}\).
\[46w+70-12{w}^{2}=0\]

6
Factor out the common term \(2\).
\[2(23w+35-6{w}^{2})=0\]

7
Factor out the negative sign.
\[2\times -(6{w}^{2}-23w-35)=0\]

8
Divide both sides by \(2\).
\[-6{w}^{2}+23w+35=0\]

9
Multiply both sides by \(-1\).
\[6{w}^{2}-23w-35=0\]

10
How?
Split the second term in \(6{w}^{2}-23w-35\) into two terms.
\[6{w}^{2}+7w-30w-35=0\]

11
Factor out common terms in the first two terms, then in the last two terms.
\[w(6w+7)-5(6w+7)=0\]

12
Factor out the common term \(6w+7\).
\[(6w+7)(w-5)=0\]

13
How?
Solve for \(w\).
\[w=-\frac{7}{6},5\]

Done

Decimal Form: -1.166667, 5