Question: Lia wants to buy some shoes. He found the shoes at three different stores for a price of $35. The stores are each having a sale.
• Store X is offering 15% off the price of the shoes.
• Store Y is offering $5 off the price of the shoes.
• Store Z is offering a 1/5 discount off the price of the shoes.
Based on this information, mark the statements below as true or false.
Store X has the best sale price of $30.
T F
Store Y has the best sale price of $30.
T F
Store Z has the best sale price of $28.
T F
Solve
1. **State the problem:**
Lia wants to buy shoes priced at $35 from three stores offering different discounts. We need to find the sale price at each store and verify the truth of the given statements.
2. **Formulas and rules:**
- Percentage discount price: $$\text{Sale Price} = \text{Original Price} - (\text{Discount Rate} \times \text{Original Price})$$
- Fixed amount discount price: $$\text{Sale Price} = \text{Original Price} - \text{Discount Amount}$$
- Fraction discount price: $$\text{Sale Price} = \text{Original Price} - \left(\frac{\text{Fraction}}{1} \times \text{Original Price}\right)$$
3. **Calculate Store X price:**
Original price = $35$
Discount = 15% = 0.15
$$\text{Sale Price}_X = 35 - (0.15 \times 35) = 35 - 5.25 = 29.75$$
4. **Calculate Store Y price:**
Discount = $5$
$$\text{Sale Price}_Y = 35 - 5 = 30$$
5. **Calculate Store Z price:**
Discount = 1/5 = 0.2
$$\text{Sale Price}_Z = 35 - (\frac{1}{5} \times 35) = 35 - 7 = 28$$
6. **Evaluate statements:**
- Store X has the best sale price of $30$: The actual price is $29.75$, so this statement is **False**.
- Store Y has the best sale price of $30$: The actual price is $30$, so this statement is **True**.
- Store Z has the best sale price of $28$: The actual price is $28$, so this statement is **True**.
**Final answers:**
- Store X: False
- Store Y: True
- Store Z: True