Higher June 2025 Paper 1 Q12
12 Oscar and Nikita share some money in the ratio 8 : 5
Oscar has £27 more than Nikita.
How much do they have altogether? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: works out the value of one share | ||
| \(27 \div (8 - 5)\) or \(27 \div 3\) or 9 | M1 | oe implied by 72 or 45 identified or used |
| their \(9 \times 8 +\) their \(9 \times 5\) or \(72 + 45\) or their \(9 \times (8 + 5)\) or their \(9 \times 13\) | M1dep | oe |
| 117 | A1 | SC1 43.81 or 43.87 or 43.88 or 43.94 |
| Alternative method 2: sets up and solves an equation | ||
| \(\dfrac{8}{5} = \dfrac{x + 27}{x}\) or \(x = 45\) or \(\dfrac{8}{5} = \dfrac{y}{y - 27}\) or \(y = 72\) or \(\dfrac{(8 - 5)w}{8 + 5} = 27\) | M1 | oe equation any letter |
| their \(45 +\) their \(45 + 27\) or their \(72 +\) their \(72 - 27\) or \(27 \times (8 + 5) \div (8 - 5)\) | M1dep | oe |
| 117 | A1 | SC1 43.81 or 43.87 or 43.88 or 43.94 |
| Alternative method 3: trial and improvement with values in the correct ratio | ||
| 8, 16, 24, 32, 40, 48, 56, 64, 72… and 5, 10, 15, 20, 25, 30, 35, 40, 45… | M1 | repeated multiples of 8 and 5 until the difference is 27 if the lists continue, 72 or 45 must be identified or used |
| \(72 + 45\) | M1dep | oe |
| 117 | A1 | SC1 43.81 or 43.87 or 43.88 or 43.94 |
Additional guidance
SC1 is for thinking Oscar has £27, with rounding at different stages