Problem of the Week

Updated at Jan 2, 2023 2:24 PM

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

How can we solve the equation \(6{(\frac{5}{4m})}^{2}=\frac{25}{24}\)?

Check out the solution below!



\[6{(\frac{5}{4m})}^{2}=\frac{25}{24}\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[6\times \frac{{5}^{2}}{{(4m)}^{2}}=\frac{25}{24}\]

2
Simplify  \({5}^{2}\)  to  \(25\).
\[6\times \frac{25}{{(4m)}^{2}}=\frac{25}{24}\]

3
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[6\times \frac{25}{{4}^{2}{m}^{2}}=\frac{25}{24}\]

4
Simplify  \({4}^{2}\)  to  \(16\).
\[6\times \frac{25}{16{m}^{2}}=\frac{25}{24}\]

5
Simplify  \(6\times \frac{25}{16{m}^{2}}\)  to  \(\frac{150}{16{m}^{2}}\).
\[\frac{150}{16{m}^{2}}=\frac{25}{24}\]

6
Simplify  \(\frac{150}{16{m}^{2}}\)  to  \(\frac{75}{8{m}^{2}}\).
\[\frac{75}{8{m}^{2}}=\frac{25}{24}\]

7
Multiply both sides by \(8{m}^{2}\).
\[75=\frac{25}{24}\times 8{m}^{2}\]

8
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[75=\frac{25\times 8{m}^{2}}{24}\]

9
Simplify  \(25\times 8{m}^{2}\)  to  \(200{m}^{2}\).
\[75=\frac{200{m}^{2}}{24}\]

10
Simplify  \(\frac{200{m}^{2}}{24}\)  to  \(\frac{25{m}^{2}}{3}\).
\[75=\frac{25{m}^{2}}{3}\]

11
Multiply both sides by \(3\).
\[75\times 3=25{m}^{2}\]

12
Simplify  \(75\times 3\)  to  \(225\).
\[225=25{m}^{2}\]

13
Divide both sides by \(25\).
\[\frac{225}{25}={m}^{2}\]

14
Simplify  \(\frac{225}{25}\)  to  \(9\).
\[9={m}^{2}\]

15
Take the square root of both sides.
\[\pm \sqrt{9}=m\]

16
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[\pm 3=m\]

17
Switch sides.
\[m=\pm 3\]

Done
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