Problem of the Week

Updated at Dec 23, 2024 3:13 PM

This week we have another equation problem:

How would you solve the equation \(\frac{20(2+4t)}{t}=90\)?

Let's start!



\[\frac{20(2+4t)}{t}=90\]

1
Factor out the common term \(2\).
\[\frac{20\times 2(1+2t)}{t}=90\]

2
Simplify  \(20\times 2(1+2t)\)  to  \(40(1+2t)\).
\[\frac{40(1+2t)}{t}=90\]

3
Multiply both sides by \(t\).
\[40(1+2t)=90t\]

4
Expand.
\[40+80t=90t\]

5
Subtract \(80t\) from both sides.
\[40=90t-80t\]

6
Simplify  \(90t-80t\)  to  \(10t\).
\[40=10t\]

7
Divide both sides by \(10\).
\[\frac{40}{10}=t\]

8
Simplify  \(\frac{40}{10}\)  to  \(4\).
\[4=t\]

9
Switch sides.
\[t=4\]

Done
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