Problem of the Week

Updated at May 11, 2020 1:03 PM

This week we have another equation problem:

How can we solve the equation \(\frac{\frac{t-3}{3}+2}{5}=\frac{7}{15}\)?

Let's start!



\[\frac{\frac{t-3}{3}+2}{5}=\frac{7}{15}\]

1
Simplify  \(\frac{t-3}{3}\)  to  \(-1+\frac{t}{3}\).
\[\frac{-1+\frac{t}{3}+2}{5}=\frac{7}{15}\]

2
Simplify  \(-1+\frac{t}{3}+2\)  to  \(\frac{t}{3}+1\).
\[\frac{\frac{t}{3}+1}{5}=\frac{7}{15}\]

3
Simplify  \(\frac{\frac{t}{3}+1}{5}\)  to  \(\frac{\frac{t}{3}}{5}+\frac{1}{5}\).
\[\frac{\frac{t}{3}}{5}+\frac{1}{5}=\frac{7}{15}\]

4
Simplify  \(\frac{\frac{t}{3}}{5}\)  to  \(\frac{t}{3\times 5}\).
\[\frac{t}{3\times 5}+\frac{1}{5}=\frac{7}{15}\]

5
Simplify  \(3\times 5\)  to  \(15\).
\[\frac{t}{15}+\frac{1}{5}=\frac{7}{15}\]

6
Subtract \(\frac{1}{5}\) from both sides.
\[\frac{t}{15}=\frac{7}{15}-\frac{1}{5}\]

7
Simplify  \(\frac{7}{15}-\frac{1}{5}\)  to  \(\frac{4}{15}\).
\[\frac{t}{15}=\frac{4}{15}\]

8
Multiply both sides by \(15\).
\[t=\frac{4}{15}\times 15\]

9
Cancel \(15\).
\[t=4\]

Done
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