Numeracy Intermediate June 2023 Unit 1 Q7
7. Mari and Huw share a prize of £2700 in the ratio 4 : 5 respectively.
Mari decides to donate 24% of her share of the prize to charity.
Huw decides to give the same amount of money as Mari to charity.
What fraction of Huw’s share of the prize money does he give to charity?
Express your answer in its simplest form.
You must show all your working. [6]
| Scheme | Marks | Comments |
|---|---|---|
| (Mari’s share of the prize) 4 × 2700 ÷ (4 + 5) OR (Huw’s share of the prize) 5 × 2700 ÷ (4 + 5) | M1 | (4 × 300) (5 × 300) |
| (Mari’s share is £) 1200 | A1 | Allow for sight of (£)1200 irrespective of the name assigned May be implied in later calculation (Huw’s share is £1500) |
| (Mari donates) 0.24 × 1200 | M1 | FT 0.24 × ‘their smaller share’ (Note: ‘their smaller share’ < 1350) |
| (£) 288 | A1 | |
| (Fraction of his prize Huw donates) 0.24 × 1200 5 × 2700 ÷ (4 + 5) or 0.24 × 1200 2700 – 1200 or 288 1500 or 1 – (1500 – 0.24 × 1200) 2700 – 1200 or 1 – 1212 1500 | M1 | FT ‘their 0.24 × ‘their smaller share’’ and 2700 – ‘their smaller share’ |
| 24 125 | A1 | Must be a simplified fraction, ISW (e.g. 19.2%) An unsimplified fraction (144/750 or 96/500 or 72/375 or 48/250) is awarded M1 A0 Only FT if there are at least 2 different common prime factors for the numerator and denominator for simplifying, and not both numerator and denominator being a multiple of 10, i.e. equivalent level of difficulty If consistently working with Mari’s getting the larger share, initially possible M1, A1 or M1, A0, but then M0, A0, M0, A0. However, also award SC2 for a final answer of \({}^{3}\!/_{10}\) or SC1 for (donation) (£)360. Mari with larger share leads to: 0.24 × 1500 2700 – 1500 = 360 1200 = 3 10 |
7. Alternative method:
| Scheme | Marks | Comments |
|---|---|---|
| (Fraction of his prize Huw donates) 4 5 × 24 100 | M3 | M2 for sight of ⅘ of 24% M1 for sight of ⅘ of 24 |
| 24 125 | A3 | Must be a simplified fraction A2 for correct unsimplified fraction, e.g. 96 500 Only FT if there are at least 2 different common prime factors for the numerator and denominator for simplifying, i.e. equivalent level of difficulty ISW (e.g. 19.2%) |
The alternative method is printed in italics in the original.