# 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$$.1 Add $$3$$ to both sides.$p=2+3$2 Simplify  $$2+3$$  to  $$5$$.$p=5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$p=5$13 Solve the 2nd equation: $$p-3=-2$$.1 Add $$3$$ to both sides.$p=-2+3$2 Simplify  $$-2+3$$  to  $$1$$.$p=1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$p=1$14 Collect all solutions.$p=5,1$Done p=5,1