Higher June 2022 Paper 2 Q15
15 The ratio of Marta’s hourly pay to Khalid’s hourly pay is 6 : 5
Both Marta and Khalid get an increase of £1.50 in their hourly pay.
The ratio of Marta’s hourly pay to Khalid’s hourly pay after this increase is 13 : 11
Work out the hourly pay before the increase for Marta and for Khalid. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| (M) 18, (K) 15 | P1 | for start of process, eg \((6x + 1.5)\) and \((5x + 1.5)\) or \((6x + 1.5)\) and \((11x + 3)\) or \(a + 1.5\) and \(b + 1.5\) OR starts to work with ratio, eg 6 : 5 = 12 : 10 |
| P1 | for setting up an equation, eg \(\dfrac{6x + 1.5}{5x + 1.5} = \dfrac{13}{11}\) or \(66x + 16.5 = 65x + 19.5\) or \(\dfrac{6x + 1.5}{11x + 3} = \dfrac{13}{24}\) or \(144x + 36 = 143x + 39\) or \(\dfrac{a}{b} = \dfrac{6}{5}\) and \(\dfrac{a + 1.5}{b + 1.5} = \dfrac{13}{11}\) or \(5a = 6b\) and \(11a + 16.5 = 13b + 19.5\) oe OR for comparing 12 : 10 to 13 : 11 and deducing 1 part = 1.5 | |
| P1 | for isolating in terms of \(x\), eg \(66x - 65x = 19.5 - 16.5\) or \(144x - 143x = 39 - 36\) or \(x = 3\) or for eliminating \(a\) or \(b\), eg \(55a = 66b\) and so \(66b = 65b + 15\) OR for process to find values for M and K, eg \(12 \times 1.5\) and \(10 \times 1.5\) | |
| A1 | cao |