Higher June 2018 Paper 1 Q26
26 \(b\) is two thirds of \(c\).
\(5a = 4c\)
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 | ||
| \(\dfrac{4}{5} : \dfrac{2}{3} : 1\) | M1 | |
| \(\dfrac{12}{15} : \dfrac{10}{15} : \dfrac{15}{15}\) | M1dep | oe common denominator implied by correct unsimplified ratio eg 24 : 20 : 30 |
| 12 : 10 : 15 | A1 | |
| Alternative method 2 | ||
| \(a : c = 4 : 5\) or \(b : c = 2 : 3\) | M1 | oe may be seen as part of a ratio with three values |
| \(a : c = 12 : 15\) and \(b : c = 10 : 15\) | M1dep | oe with \(c\) values equal |
| 12 : 10 : 15 | A1 | |
| Alternative method 3 | ||
| (\(5a =\)) \(6b = 4c\) or \(1 : \dfrac{5}{6} : \dfrac{5}{4}\) or \(\dfrac{6}{5} : 1 : \dfrac{6}{4}\) | M1 | oe ratio |
| \(\dfrac{12}{12} : \dfrac{10}{12} : \dfrac{15}{12}\) or \(\dfrac{24}{20} : \dfrac{20}{20} : \dfrac{30}{20}\) | M1dep | oe common denominator implied by correct unsimplified ratio eg 24 : 20 : 30 |
| 12 : 10 : 15 | A1 | |
| Alternative method 4 | ||
| Picks values so that \(a\) is four fifths of \(c\) and \(b\) is two thirds of \(c\) | M1 | eg (\(a =\)) 60, (\(b =\)) 50, (\(c =\)) 75 (\(a =\)) 4, (\(b =\)) \(\dfrac{10}{3}\), (\(c =\)) 5 |
| Correct ratio for their values as integers or fractions with a common denominator | M1dep | eg 60 : 50 : 75 or \(\dfrac{12}{3} : \dfrac{10}{3} : \dfrac{15}{3}\) |
| 12 : 10 : 15 | A1 | |