Higher November 2024 Paper 2 Q12
12 At a music festival, four types of instrument are played.
guitars keyboards drums trumpets
- The total number of instruments is 80
- Half of the instruments are guitars.
- keyboards : drums : trumpets = 3 : 4 : 1
How many keyboards are there? [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| (guitars =) \(80 \div 2\) or 40 | M1 | oe |
| their \(40 \div (3 + 4 + 1)\) or 5 | M1dep | oe |
| \(3 \times\) their 5 | M1dep | oe \(\dfrac{3}{3 + 4 + 1} \times 40\) is M3 |
| 15 | A1 | |
| Alternative method 2 | ||
| \(80 \div (3 + 4 + 1)\) or 10 | M1 | oe |
| \(3 \times\) their 10 or 30 | M1dep | oe |
| their \(30 \div 2\) | M1dep | oe |
| 15 | A1 | |
| Alternative method 3 | ||
| (guitars =) \(80 \div 2\) or 40 | M1 | oe |
| \(x + \dfrac{4}{3}x + \dfrac{1}{3}x =\) their 40 | M1dep | oe equation with \(x\) as number of keyboards |
| \(\dfrac{14}{3}x =\) their 40 | M1dep | oe equation in form \(ax = b\) |
| 15 | 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
Other algebraic approaches are possible
eg (guitars =) \(80 \div 2\) or 40 M1
\(3x + 4x + x =\) their 40
but does not score 2nd M1 until \((x =)\) their \(40 \div (3 + 4 + 1)\)