Problem of the Week

Updated at Oct 12, 2026 8:59 AM

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

How would you solve \(\frac{4}{2(5+\frac{5}{t})}=\frac{4}{15}\)?

Check out the solution below!



\[\frac{4}{2(5+\frac{5}{t})}=\frac{4}{15}\]

1
Factor out the common term \(5\).
\[\frac{4}{2\times 5(1+\frac{1}{t})}=\frac{4}{15}\]

2
Simplify  \(2\times 5(1+\frac{1}{t})\)  to  \(10(1+\frac{1}{t})\).
\[\frac{4}{10(1+\frac{1}{t})}=\frac{4}{15}\]

3
Simplify  \(\frac{4}{10(1+\frac{1}{t})}\)  to  \(\frac{2}{5(1+\frac{1}{t})}\).
\[\frac{2}{5(1+\frac{1}{t})}=\frac{4}{15}\]

4
Multiply both sides by \(5(1+\frac{1}{t})\).
\[2=\frac{4}{15}\times 5(1+\frac{1}{t})\]

5
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[2=\frac{4\times 5(1+\frac{1}{t})}{15}\]

6
Simplify  \(4\times 5(1+\frac{1}{t})\)  to  \(20(1+\frac{1}{t})\).
\[2=\frac{20(1+\frac{1}{t})}{15}\]

7
Simplify  \(\frac{20(1+\frac{1}{t})}{15}\)  to  \(\frac{4}{3}(1+\frac{1}{t})\).
\[2=\frac{4}{3}(1+\frac{1}{t})\]

8
Divide both sides by \(4\).
\[\frac{2}{4}=\frac{1}{3}(1+\frac{1}{t})\]

9
Simplify  \(\frac{2}{4}\)  to  \(\frac{1}{2}\).
\[\frac{1}{2}=\frac{1}{3}(1+\frac{1}{t})\]

10
Simplify  \(\frac{1+\frac{1}{t}}{3}\)  to  \(\frac{1}{3}+\frac{\frac{1}{t}}{3}\).
\[\frac{1}{2}=\frac{1}{3}+\frac{\frac{1}{t}}{3}\]

11
Simplify  \(\frac{\frac{1}{t}}{3}\)  to  \(\frac{1}{3t}\).
\[\frac{1}{2}=\frac{1}{3}+\frac{1}{3t}\]

12
Subtract \(\frac{1}{3}\) from both sides.
\[\frac{1}{2}-\frac{1}{3}=\frac{1}{3t}\]

13
Simplify  \(\frac{1}{2}-\frac{1}{3}\)  to  \(\frac{1}{6}\).
\[\frac{1}{6}=\frac{1}{3t}\]

14
Multiply both sides by \(3t\).
\[\frac{1}{6}\times 3t=1\]

15
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{1\times 3t}{6}=1\]

16
Simplify  \(1\times 3t\)  to  \(3t\).
\[\frac{3t}{6}=1\]

17
Simplify  \(\frac{3t}{6}\)  to  \(\frac{t}{2}\).
\[\frac{t}{2}=1\]

18
Multiply both sides by \(2\).
\[t=1\times 2\]

19
Simplify  \(1\times 2\)  to  \(2\).
\[t=2\]

Done
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