Foundation November 2022 Paper 2 Q19
19 On a train, there are between 60 and 70 people.
The ratio of adults to children is \(\;5 : 4\)
Work out the total number of people on the train. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| Pair of integers in the ratio \(5 : 4\) between \(20 : 16\) and \(75 : 60\) or list of multiples of 9 with at least 3 correct including 63 or \(63 \div 9 = 7\) or \(63 \div 7 = 9\) or \(9 \times 7 = 63\) | M1 | 20 and 16 or 25 and 20 or 30 and 24 or 35 and 28 or 40 and 32 or 45 and 36 or 50 and 40 or 55 and 44 or 60 and 48 or 65 and 52 or 70 and 56 or 75 and 60 |
| 63 | A1 | |
| Alternative method 2 | ||
| An integer \([60, 70]\) divided in the ratio \(5 : 4\) eg \(65 \div 9 \times 5\) and \(65 \div 9 \times 4\) | M1 | if no method seen, values must be rounded or truncated to at least 1 dp eg 65 and 36.1 and 28.8 or 28.9 |
| 63 | A1 | |
Additional guidance
| Up to M1 may be awarded for correct work with no answer, or incorrect answer, even if this is seen amongst multiple attempts | |
| M1 pairs of responses may be seen in a ratio | |
| Answer \(35 : 28\) | M1A0 |
| 63 seen in list of multiples eg 27, 36, 45, 54, 63, … but not selected as the answer | M1A0 |
| 63 from incorrect method with no M1 response seen | M0A0 |
| Alt 2 eg \(65 \div 9 = 7.2\) with 36 and 28.8 implies multiplication by 5 and 4 (because it follows through from their answer to the correct division) | M1A0 |
| Alt 2 eg \(65 \div 9 = 7.2\) with 36.1 and 28.8 or 28.9 implies multiplication by 5 and 4 (may have kept full value on calculator) | M1A0 |
| Alt 2 eg 65 and no working with 36 and 28.8 does not imply the method (because these are not rounded or truncated to at least 1 dp) | M0A0 |