1. **State the problem:** Lucy sold 4 scarves for the same amount each and then spent 10.50 of her total earnings on a sweater. After that, she had 7.50 left. We need to find the value of each scarf. 2. **Define variables:** Let $x$ be the amount of money Lucy received for each scarf. 3. **Write the equation:** Total earnings from scarves is $4x$. After spending 10.50, she has 7.50 left, so: $$4x - 10.50 = 7.50$$ 4. **Solve the equation:** Add 10.50 to both sides: $$4x = 7.50 + 10.50$$ $$4x = 18.00$$ Divide both sides by 4: $$x = \frac{18.00}{4}$$ $$x = 4.50$$ 5. **Interpret the result:** Each scarf was sold for 4.50. **Final answer:** Each scarf was worth $4.50.