Shopping Expenses
1. **State the problem:** Calculate the weighted average price per unit of items purchased and explain why the weighted average is more meaningful than the simple average in this context.
2. **List given data:**
- Rice: price = 60, quantity = 5
- Lentils: price = 120, quantity = 2
- Oil: price = 150, quantity = 1
- Sugar: price = 80, quantity = 3
3. **Calculate total cost:**
$$\text{Total cost} = (60 \times 5) + (120 \times 2) + (150 \times 1) + (80 \times 3)$$
$$= 300 + 240 + 150 + 240 = 930$$
4. **Calculate total quantity:**
$$\text{Total quantity} = 5 + 2 + 1 + 3 = 11$$
5. **Calculate weighted average price per unit:**
$$\text{Weighted average price} = \frac{\text{Total cost}}{\text{Total quantity}} = \frac{930}{11} \approx 84.55$$
6. **Explain why weighted average is more meaningful:**
The weighted average takes into account the quantity of each item bought, reflecting the true average price paid per unit. A simple average would just average the prices without considering how much of each item was purchased, which could misrepresent the overall spending.
**Final answer:** The weighted average price per unit is approximately $84.55$.