Lucy brought 4 of her scarves to a secondhand store to sell. She was paid the same amount of cash for each scarf. Before she left, Lucy spent $10.50 of her earnings on a used sweater. She had $7.50 remaining. What was the value of each scarf?

Answer 1

Let $x$ be the amount Lucy was paid for each scarf. Since she brought 4 scarves, the total earnings from selling the scarves can be calculated as:

$$4x$$

After selling the scarves, Lucy spent $10.50 on a used sweater, and she was left with $7.50. Thus, we can express this situation with the following equation:

$$4x-10.50=7.50$$

To solve for $x$, we first add $10.50 to both sides of the equation:

$$4x=7.50+10.50$$

Calculating the right side gives:

$$4x=18.00$$

Next, we divide both sides by 4 to find $x$:

$$x=\frac{18.00}{4}=4.50$$

Thus, the value of each scarf is

$$\boxed{{\displaystyle 4.50}}$$