Higher June 2024 Paper 2 Q21
21 People in a stadium are in the North Stand, East Stand, South Stand or West Stand.
Of the people in the stadium,
- \(\dfrac{1}{4}\) are in the North Stand
- \(\dfrac{3}{10}\) are in the East Stand
- number in South Stand : number in West Stand \(= 2 : 7\)
There are 4480 people in the West Stand.
How many people are in the stadium? [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: uses total and proportion in S with W | ||
| \(4480 \times \dfrac{9}{7}\) or 5760 | M1 | oe total in S with W eg \(640 \times 9\) |
| \(1 - \dfrac{1}{4} - \dfrac{3}{10}\) or \(\dfrac{9}{20}\) | M1 | oe proportion in S with W eg 0.45 or 45% |
| their 5760 \(\div\) their \(\dfrac{9}{20}\) | M1dep | oe full method dep on M2 |
| 12 800 | A1 | |
| Alternative method 2: uses total in S with W and total in N with E | ||
| \(4480 \times \dfrac{9}{7}\) or 5760 | M1 | oe total in S with W eg \(640 \times 9\) |
| \(4480 \times \dfrac{11}{7}\) or 7040 | M1 | oe total in N with E eg \(640 \times 11\) |
| their 5760 \(+\) their 7040 | M1dep | oe full method eg \(640 \times 20\) dep on M2 |
| 12 800 | A1 | |
| Alternative method 3: sets up an equation | ||
| \(4480 \times \dfrac{9}{7}\) or 5760 | M1 | oe total in S with W eg \(640 \times 9\) |
| \(\dfrac{1}{4}x + \dfrac{3}{10}x +\) their \(5760 = x\) | M1dep | oe equation in any variable eg \(10x + 12x + 230\,400 = 40x\) |
| their 5760 \(\div \left(1 - \dfrac{1}{4} - \dfrac{3}{10}\right)\) | M1dep | oe full method eg \(230\,400 \div 18\) |
| 12 800 | A1 | |
| Alternative method 4: works out proportion in W or proportion in S | ||
| \(1 - \dfrac{1}{4} - \dfrac{3}{10}\) or \(\dfrac{9}{20}\) | M1 | oe proportion in S with W eg 0.45 or 45% |
| \(\dfrac{7}{9} \times\) their \(\dfrac{9}{20}\) or \(\dfrac{7}{20}\) or \(\dfrac{2}{9} \times\) their \(\dfrac{9}{20}\) or \(\dfrac{2}{20}\) | M1dep | oe proportion in W eg 0.35 or 35% eg \(\dfrac{7}{7 + 2} \times\) their \(\dfrac{9}{20}\) or oe proportion in S eg 0.1 or 10% eg \(\dfrac{2}{7 + 2} \times\) their \(\dfrac{9}{20}\) |
| \(4480 \div\) their \(\dfrac{7}{20}\) or \(4480 \times \dfrac{2}{7} \div\) their \(\dfrac{2}{20}\) | M1dep | oe full method eg \(640 \times 20\) |
| 12 800 | 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
Proportions can be percentages but in calculations values must be used
eg Alt 1 \(5760 \div 45\%\) is awarded M2 but cannot be awarded the 3rd M1
unless \(\dfrac{9}{20}\) or 0.45 is subsequently used correctly