Higher June 2017 Paper 3 Q11
11 Purple paint is made by mixing red paint and blue paint in the ratio 5 : 2
Yan has 30 litres of red paint and 9 litres of blue paint.
What is the maximum amount of purple paint he can make? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| Any correct scaling of the ratio 5 : 2 eg 10 (:) 4 or 20 (:) 8 or 25 (:) 10 | M1 | oe |
| 22.5 (:) 9 or 22.5 (red) or 30 (:) 12 or 12 (blue) | M1dep | oe |
| 31.5 or \(31\dfrac{1}{2}\) or \(\dfrac{63}{2}\) | A1 | |
| Alternative method 2 | ||
| \(9 \div 2\) or 4.5 or \(30 \div 5\) or 6 | M1 | oe \(2 \div 9\) or 0.22… \(5 \div 30\) or 0.16… or 0.17 |
| \(5 \times\) their 4.5 or 22.5 or \(7 \times\) their 4.5 or \(2 \times\) their 6 or 12 or \(7 \times\) their 6 or 42 | M1dep | oe |
| 31.5 or \(31\dfrac{1}{2}\) or \(\dfrac{63}{2}\) | A1 | |
| Alternative method 3 | ||
| \(\dfrac{2}{7} \times\) purple = blue \(\dfrac{5}{7} \times\) purple = red | M1 | oe \(\;\dfrac{2}{7} \times\) purple = 9 \(\dfrac{5}{7} \times\) purple = 30 |
| \(9 \times \dfrac{7}{2}\) or \(30 \times \dfrac{7}{5}\) or 42 | M1dep | oe |
| 31.5 or \(31\dfrac{1}{2}\) or \(\dfrac{63}{2}\) | A1 | |
Additional guidance
| 28 + 3.5 = 31.5 | M1M1A1 |
| 28 + 3.5 | M1M1A0 |
| 31.5, answer 31 | M1M1A1 |
| 31.5 + 42 = 73.5 | M1M1A0 |
| 10 4 | M1M0A0 |
| 10, 4 | M1M0A0 |
| 10 + 4 | M1M0A0 |
| ‘He has 2.5 times more red than blue’ | M1M0A0 |
| 2.5 : 1 | M1M0A0 |
| 2.5 | M0M0A0 |
| 28 on its own | M0M0A0 |