Question: A car dealership offers two types of discounts. The car has an original price of $22,860. A rebate means you get that money back (so subtract)
• Discount 1: Take 5% off the original price and then receive a $3,500 rebate.
• Discount 2: Take 10% off the original price of a car built this year and then receive a $1,250 rebate.
Based on this information, mark the statements below as true or false.
The customer would pay $21,824 for the car.
T F
The customer would pay $19,324 for the car.
T F
The customer would pay $23,107 for the car.
T F
1. **State the problem:** We need to determine the final price a customer pays after applying two different discount options to a car originally priced at $22,860.
2. **Formulas and rules:**
- Discounted price after percentage discount = Original price $\times$ (1 - discount rate)
- Final price after rebate = Discounted price - rebate amount
3. **Calculate Discount 1:**
- 5% off means discount rate = $0.05$
- Discounted price = $$22,860 \times (1 - 0.05) = 22,860 \times 0.95 = 21,717$$
- Final price after $3,500 rebate = $$21,717 - 3,500 = 18,217$$
4. **Calculate Discount 2:**
- 10% off means discount rate = $0.10$
- Discounted price = $$22,860 \times (1 - 0.10) = 22,860 \times 0.90 = 20,574$$
- Final price after $1,250 rebate = $$20,574 - 1,250 = 19,324$$
5. **Evaluate the statements:**
- Customer pays $21,824: Compare with both final prices $18,217$ and $19,324$. Neither matches $21,824$, so **False**.
- Customer pays $19,324: This matches Discount 2 final price exactly, so **True**.
- Customer pays $23,107: This is higher than original price, no discount results in this, so **False**.
**Final answers:**
- $21,824$ → False
- $19,324$ → True
- $23,107$ → False