Question

practice solving linear equations in one variable with the variable on both sides
a shoe store sells a pair of sandals that cost \\(\frac{1}{4}\\) as much as a pair of sneakers. when the sneakers are discounted by $20, the sandals cost \\(\frac{1}{2}\\) as much as the pair of sneakers. the equation \\(\frac{1}{4}p = \frac{1}{2}(p - 20)\\) represents the situation, where \\(p\\) is the price of the sneakers before the discount.
choose one option from each drop - down menu to write a true statement.
before the discount, the sneakers cost $
after the $20 discount, the sneakers cost $
the sandals cost $

Explanation:

Step1: Solve the equation $\frac{1}{4}p=\frac{1}{2}(p - 20)$

First, distribute the $\frac{1}{2}$ on the right side: $\frac{1}{4}p=\frac{1}{2}p-10$
Then, subtract $\frac{1}{4}p$ from both sides: $0=\frac{1}{2}p-\frac{1}{4}p - 10$
Simplify the right side: $0=\frac{1}{4}p - 10$
Add 10 to both sides: $\frac{1}{4}p = 10$
Multiply both sides by 4: $p = 40$

Step2: Find the price after discount

The price after discount is $p - 20$, substitute $p = 40$: $40 - 20 = 20$

Step3: Find the price of sandals

The price of sandals is $\frac{1}{4}p$, substitute $p = 40$: $\frac{1}{4}\times40 = 10$

Answer:

Before the discount, the sneakers cost $\$40$.
After the $\$20$ discount, the sneakers cost $\$20$.
The sandals cost $\$10$.