Question: User: 5. Buying full boxes only
A hall needs 1125 floor tiles.
Tiles are sold only in full boxes of 48 tiles. Each box costs $18.75 and the delivery costs $24.60
a) How many boxes must be bought?
b) How many extra tiles will there be?
c) What is the total cost?
1. **State the problem:**
A hall requires $1125$ floor tiles. Tiles are sold only in full boxes, each containing $48$ tiles. Each box costs $18.75$ and delivery costs $24.60$. We need to find:
a) The number of boxes to buy.
b) The number of extra tiles after buying full boxes.
c) The total cost including delivery.
2. **Calculate the number of boxes needed:**
Since tiles come in boxes of $48$, the number of boxes needed is the smallest integer greater than or equal to $\frac{1125}{48}$.
$$\frac{1125}{48} = 23.4375$$
Since we cannot buy partial boxes, we round up:
$$\text{boxes} = \lceil 23.4375 \rceil = 24$$
3. **Calculate the number of extra tiles:**
Total tiles bought = $24 \times 48 = 1152$
Extra tiles = $1152 - 1125 = 27$
4. **Calculate the total cost:**
Cost of boxes = $24 \times 18.75$
$$24 \times 18.75 = 450$$
Add delivery cost:
$$450 + 24.60 = 474.60$$
**Final answers:**
- a) $24$ boxes
- b) $27$ extra tiles
- c) Total cost is $474.60$