Numeracy Higher November 2021 Unit 1 Q3
3. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Sara makes handmade chocolates.
She sells the chocolates in boxes.
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.
Sara makes 20% profit from selling all 150 boxes of chocolates.
How much profit does Sara make?
You must show all your working. [6 + 2 OCW]
| Scheme | Marks | Comments |
|---|---|---|
| 3. For all methods | If an evaluation is given with incorrect units, award A0 on the first occasion then FT | |
| 3. (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 |
| Organisation and communication | OC1 | For OC1, candidates will be expected to: • present their response in a structured way • explain to the reader what they are doing at each step of their response • lay out their explanations and working in a way that is clear and logical • write a conclusion that draws together their results and explains what their answer means |
| Writing | W1 | For W1, candidates will be expected to: • show all their working • make few, if any, errors in spelling, punctuation and grammar • use correct mathematical form in their working • use appropriate terminology, units, etc. |
3. 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 |
3. 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 |
3. 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 |
3. 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 |
3. 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 |