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(54m)2=25246{(\frac{5}{4m})}^{2}=\frac{25}{24}?

Check out the solution below!



6(54m)2=25246{(\frac{5}{4m})}^{2}=\frac{25}{24}

1
Use Division Distributive Property: (xy)a=xaya{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}.
6×52(4m)2=25246\times \frac{{5}^{2}}{{(4m)}^{2}}=\frac{25}{24}

2
Simplify  52{5}^{2}  to  2525.
6×25(4m)2=25246\times \frac{25}{{(4m)}^{2}}=\frac{25}{24}

3
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
6×2542m2=25246\times \frac{25}{{4}^{2}{m}^{2}}=\frac{25}{24}

4
Simplify  42{4}^{2}  to  1616.
6×2516m2=25246\times \frac{25}{16{m}^{2}}=\frac{25}{24}

5
Simplify  6×2516m26\times \frac{25}{16{m}^{2}}  to  15016m2\frac{150}{16{m}^{2}}.
15016m2=2524\frac{150}{16{m}^{2}}=\frac{25}{24}

6
Simplify  15016m2\frac{150}{16{m}^{2}}  to  758m2\frac{75}{8{m}^{2}}.
758m2=2524\frac{75}{8{m}^{2}}=\frac{25}{24}

7
Multiply both sides by 8m28{m}^{2}.
75=2524×8m275=\frac{25}{24}\times 8{m}^{2}

8
Use this rule: ab×cd=acbd\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}.
75=25×8m22475=\frac{25\times 8{m}^{2}}{24}

9
Simplify  25×8m225\times 8{m}^{2}  to  200m2200{m}^{2}.
75=200m22475=\frac{200{m}^{2}}{24}

10
Simplify  200m224\frac{200{m}^{2}}{24}  to  25m23\frac{25{m}^{2}}{3}.
75=25m2375=\frac{25{m}^{2}}{3}

11
Multiply both sides by 33.
75×3=25m275\times 3=25{m}^{2}

12
Simplify  75×375\times 3  to  225225.
225=25m2225=25{m}^{2}

13
Divide both sides by 2525.
22525=m2\frac{225}{25}={m}^{2}

14
Simplify  22525\frac{225}{25}  to  99.
9=m29={m}^{2}

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

16
Since 3×3=93\times 3=9, the square root of 99 is 33.
±3=m\pm 3=m

17
Switch sides.
m=±3m=\pm 3

Done
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