Courtyard Paving and Edging
A school is replacing the paving in a rectangular courtyard measuring 7.5 m by 4.8 m. In one corner there is a rectangular planting bed 2.4 m by 1.5 m that will remain unpaved. The new paving slabs are square, 50 cm by 50 cm, and are sold only in packs of 10. The site manager requires 8% extra slabs on top of the exact area calculation before rounding up to whole packs, and the school does not want to keep more than one pack of unused slabs after the job. Each pack costs £24.50. A supplier offers 15% off the paving pack total if the school buys 15 packs or more. Edging for the boundary of the paved area is sold in 2.4 m lengths at £9.80 each; the boundary includes the edges around the planting bed. The business manager wants the lowest total cost that still meets the 8% spare requirement.
1. Calculate the paved area and the minimum number of slabs needed, including the 8% allowance. How many packs must be bought, and what is the cost before any discount?
Read the worked answer
Courtyard area = 7.5 × 4.8 = 36 m². Bed area = 2.4 × 1.5 = 3.6 m². Paved area = 36 − 3.6 = 32.4 m². Each slab area = 0.5 × 0.5 = 0.25 m². Exact slab count = 32.4 ÷ 0.25 = 129.6. With 8% extra on the exact area calculation: 32.4 × 1.08 = 34.992 m², and 34.992 ÷ 0.25 = 139.968, so 140 slabs are needed. Packs of 10 give 140 ÷ 10 = 14 packs. Cost = 14 × £24.50 = £343.00.
2. Calculate the length of edging needed around the paved area. How many 2.4 m lengths must be bought, and what is the edging cost?
Read the worked answer
Since the bed is in a corner, it removes 2.4 + 1.5 = 3.9 m from the outer courtyard boundary but adds the same 3.9 m as inner edges around the bed. The paved boundary therefore equals the courtyard perimeter: 2(7.5 + 4.8) = 24.6 m. Each edging length is 2.4 m, so 24.6 ÷ 2.4 = 10.25, requiring 11 lengths. Edging cost = 11 × £9.80 = £107.80.
3. Compare buying 14 packs at full price with 15 packs at the 15% discount. Which option gives the lower paving cost, and does it leave an acceptable number of unused slabs?
Read the worked answer
14 packs cost 14 × £24.50 = £343.00. 15 packs cost 15 × £24.50 = £367.50, less 15%: 367.50 × 0.85 = £312.375, i.e. £312.38 to the nearest penny. 15 packs give 150 slabs; 140 are required, leaving 10 slabs, which is one pack. That satisfies the 'no more than one pack unused' condition. The 15-pack offer is cheaper by 343.00 − 312.38 = £30.62, so the school should take it. With edging, total cost is £312.38 + £107.80 = £420.18.