Problem of the Week

Updated at Oct 16, 2023 12:46 PM

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

How would you solve the equation \(\frac{{(\frac{p-3}{5})}^{2}}{6}=\frac{2}{75}\)?

Here are the steps:



\[\frac{{(\frac{p-3}{5})}^{2}}{6}=\frac{2}{75}\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{{(p-3)}^{2}}{{5}^{2}}}{6}=\frac{2}{75}\]

2
Simplify  \({5}^{2}\)  to  \(25\).
\[\frac{\frac{{(p-3)}^{2}}{25}}{6}=\frac{2}{75}\]

3
Simplify  \(\frac{\frac{{(p-3)}^{2}}{25}}{6}\)  to  \(\frac{{(p-3)}^{2}}{25\times 6}\).
\[\frac{{(p-3)}^{2}}{25\times 6}=\frac{2}{75}\]

4
Simplify  \(25\times 6\)  to  \(150\).
\[\frac{{(p-3)}^{2}}{150}=\frac{2}{75}\]

5
Multiply both sides by \(150\).
\[{(p-3)}^{2}=\frac{2}{75}\times 150\]

6
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[{(p-3)}^{2}=\frac{2\times 150}{75}\]

7
Simplify  \(2\times 150\)  to  \(300\).
\[{(p-3)}^{2}=\frac{300}{75}\]

8
Simplify  \(\frac{300}{75}\)  to  \(4\).
\[{(p-3)}^{2}=4\]

9
Take the square root of both sides.
\[p-3=\pm \sqrt{4}\]

10
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[p-3=\pm 2\]

11
Break down the problem into these 2 equations.
\[p-3=2\]
\[p-3=-2\]

12
Solve the 1st equation: \(p-3=2\).
\[p=5\]

13
Solve the 2nd equation: \(p-3=-2\).
\[p=1\]

14
Collect all solutions.
\[p=5,1\]

Done
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