Foundation June 2017 Paper 1 Q18
18. The diagram shows a rectangular garden, ABCD.
The garden is to be enclosed by a wire fence.
There must be a gap of 2 m for the gate.
Wire fencing costs
- £32 for a whole 10 m roll
- £4.50 per metre
Diagram not drawn to scale
Work out the cheapest cost of enclosing the garden with this wire fencing.
Justify your answer. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (length of fencing needed =) 5 + 10 + 5 + 8 oe or 28 | B1 | Allow this to be seen or implied by eg working to find 2 rolls and 8 metres or 3 rolls and 2 metres |
| (3 full rolls cost) 3 × 32 = (£)96 or equivalent | M1 | |
| (8 metres cost ) 4.5(0) × 8 = (£)36 or (28 metres cost ) 4.5(0) × 28 = (£)126 or (2 rolls and 8 metres cost) 2 × 32 + 4.5(0) × 8 = (£)100 or valid alternative | M1 | Justification that a whole roll is cheaper than 8 single metres May be implied by sight of 64 + 36 FT ‘their derived 8’ |
| Concluding (£)96 is the cheapest cost after finding the cost of 8 metres (£36) or 2 rolls and 8 metres (£100) | A1 | Allow 3 full rolls is cheapest if the (£)96 was obtained earlier. |
| (4) |