Higher November 2023 Paper 3 Q25
25 \(a\) is three quarters of \(c\)
\(6b = 5c\)
Work out the ratio \(\quad a : b : c\)
Give your answer in its simplest form, where \(a\), \(b\) and \(c\) are integers. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{3}{4} : \dfrac{5}{6} : 1\) | M1 | oe ratio with one value = 1 |
| \(\dfrac{18}{24} : \dfrac{20}{24} : \dfrac{24}{24}\) | M1dep | oe ratio with common denominators implied by ratio with integers not in simplest form |
| 9 : 10 : 12 | A1 | |
| Alternative method 2 | ||
| \(a : c = 3 : 4\) and \(b : c = 5 : 6\) | M1 | oe |
| \(a : c = 9 : 12\) and \(b : c = 10 : 12\) | M1dep | oe with \(c\) values equal |
| 9 : 10 : 12 | A1 | |
| Alternative method 3 | ||
| Values such that \(a\) is three quarters of \(c\) and \(6b = 5c\) | M1 | eg \((a =)\ 45 \quad (b =)\ 50 \quad (c =)\ 60\) or \((a =)\ 3 \quad (b =)\ \dfrac{10}{3} \quad (c =)\ 4\) |
| Correct ratio for their values as integers, decimals or fractions with a common denominator | M1dep | 45 : 50 : 60 or \(\dfrac{9}{3} : \dfrac{10}{3} : \dfrac{12}{3}\) implies M2 |
| 9 : 10 : 12 | A1 | |
Additional guidance
| Up to M2 may be awarded for correct work, with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| 18 : 20 : 24 or 4.5 : 5 : 6 | M1M1A0 |
| 0.9 : 1 : 1.2 | M1M1A0 |