Numeracy Intermediate November 2021 Unit 1 Q8
8. Sara makes and sells handmade chocolates.
(a) She makes boxes for her chocolates in the shape of a tetrahedron.
Sara uses thin card to make each box.
The length of each edge of the box is 5 cm.
Sara uses thin card to make each box.
The length of each edge of the box is 5 cm.
What is the total length of the edges of one box?
Circle your answer. [1]
15 cm 30 cm 40 cm 45 cm 60 cm
(b) Each box contains 4 chocolates.
Each chocolate costs Sara 7p to make.
She can make 25 boxes from thin card for 50p.
Sara makes just enough chocolates and boxes to sell 150 boxes of chocolates.
Each chocolate costs Sara 7p to make.
She can make 25 boxes from thin card for 50p.
Sara makes just enough chocolates and boxes to sell 150 boxes of chocolates.
Sara makes 20% profit from selling all 150 boxes of chocolates.
How much profit does Sara make?
You must show all your working. [6]
| Scheme | Marks | Comments |
|---|---|---|
| 30 cm | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| For all methods | If an evaluation is given with incorrect units, award A0 on the first occasion then FT | |
| (Cost to make 150 boxes) (150 ÷ 25) ÷ 2 or 6 × 50 or equivalent | M1 | |
| (£)3 or 300(p) | A1 | |
| (Cost of the chocolates) 150 × 4 × 7 or 600 × 7 or equivalent | M1 | |
| 4200(p) or (£) 42 | A1 | |
| (Profit) 0.2 × (3 + 42) or equivalent | M1 | FT 0.2 × (‘their cost of boxes + their cost of chocolates’) |
| (£) 9 or 900(p) | A1 | ISW |
8(b) Alternative method 1:
| Scheme | Marks | Comments |
|---|---|---|
| (Each box of chocolates costs) 4 × 7 + 50 ÷ 25 | M1 | |
| 30(p) | A1 | |
| (Each box of chocolates sells for) 30 × 1.2 | M1 | FT ‘their derived 30p’ (including omitting the box) |
| 36(p) | A1 | |
| (Profit) (36 – 30) × 150 | M1 | FT 150 × ‘individual (sales – cost)’ |
| (£)9 or 900(p) | A1 | ISW |
8(b) Alternative method 2:
| Scheme | Marks | Comments |
|---|---|---|
| (Each box of chocolates costs) 4 × 7 + 50 ÷ 25 | M1 | |
| 30(p) | A1 | |
| (Profit for one box of chocolates) 30 × 0.2 | M1 | FT ‘their derived 30p’ (including omitting the box) |
| 6(p) | A1 | |
| (Profit) 6 × 150 | M1 | FT 150 × ‘their profit per box’ |
| (£)9 or 900(p) | A1 | ISW |
8(b) Alternative method 3:
| Scheme | Marks | Comments |
|---|---|---|
| (25 boxes of chocolates cost) 4 × 7 × 25 + 50 | M1 | |
| 750 (p) or (£)7.50 | A1 | |
| (Profit for 25 boxes of chocolates) 7(.)50 × 0.2 | M1 | FT ‘their derived 7(.)50’ (including omitting the box) |
| (£)1.50 or 150(p) | A1 | |
| (Profit) 1(.)50 × 150 ÷ 25 | M1 | FT ‘their profit for 25 boxes’ × 150 ÷ 25 |
| (£)9 or 900(p) | A1 | ISW |
8(b) Alternative method 4:
| Scheme | Marks | Comments |
|---|---|---|
| (25 boxes of chocolates cost) 4 × 7 × 25 + 50 | M1 | |
| 750 (p) or (£)7.50 | A1 | |
| (Total cost to make) 7(.)50 × 150 ÷ 25 | M1 | FT ‘their derived 7(.)50’ (including omitting the box) |
| (£)45 or 4500(p) | A1 | |
| (Profit) 45 × 0.2 or 4500 × 0.2 | M1 | FT 0.2 × ‘their total cost to make’ |
| (£)9 or 900(p) | A1 | ISW |
8(b) Alternative method 5:
| Scheme | Marks | Comments |
|---|---|---|
| (Each box of chocolates costs) 4 × 7 + 50 ÷ 25 | M1 | |
| 30(p) | A1 | |
| (Total cost to make) (0.)30 × 150 | M1 | FT ‘their derived 30p’ (including omitting the box) |
| (£)45 or 4500(p) | A1 | |
| (Profit) 45 × 0.2 or 4500 × 0.2 | M1 | FT 0.2 × ‘their total cost to make’ |
| (£)9 or 900(p) | A1 | ISW |
The alternative methods are printed in italics in the original.