Higher November 2017 Paper 3 Q24
24 \(a : b = 9 : 4 \quad\) and \(\quad 10b = 7c\)
Work out \(\;a : c\;\) in its simplest form. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(4a = 9b\) | M1 | oe \(\dfrac{a}{b} = \dfrac{9}{4}\) |
| \(4a = 9 \times \dfrac{7c}{10}\) or \(40a = 63c\) or \(40a = 90b\) and \(90b = 63c\) | M1dep | oe \(9 : \dfrac{40}{7}\) |
| 63 : 40 | A1 | Accept \(\dfrac{63}{40} : 1\) or 1.575 : 1 or \(1 : \dfrac{40}{63}\) |
| Alternative method 2 | ||
| \(b : c = 7 : 10\) | M1 | |
| \(a : b = 63 : 90\) and \(b : c = 90 : 40\) or 63 : 90 : 40 | M1dep | oe common value for \(b\) |
| 63 : 40 | A1 | Accept \(\dfrac{63}{40} : 1\) or 1.575 : 1 or \(1 : \dfrac{40}{63}\) |
| Alternative method 3 | ||
| \(a = \dfrac{9b}{4}\) or \(c = \dfrac{10b}{7}\) | M1 | |
| \(\dfrac{9b}{4} : \dfrac{10b}{7}\) or \(\dfrac{9}{4} : \dfrac{10}{7}\) | M1dep | oe |
| 63 : 40 | A1 | Accept \(\dfrac{63}{40} : 1\) or 1.575 : 1 or \(1 : \dfrac{40}{63}\) |
| Alternative method 4 | ||
| \(c = \dfrac{10}{7}b\) | M1 | eg \(a : c = a : \dfrac{10}{7}b\) |
| \(9 : \dfrac{10}{7} \times 4\) or \(9 : \dfrac{40}{7}\) | M1dep | oe |
| 63 : 40 | A1 | Accept \(\dfrac{63}{40} : 1\) or 1.575 : 1 or \(1 : \dfrac{40}{63}\) |
Additional guidance
| 2nd method mark is for a link between \(a\) and \(c\) or a correct ratio in an unsimplified form | |
| 40 : 63 on answer line | M1M1A0 |