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

\[ \boxed{4.50} \]