Foundation November 2019 Paper 1 Q20
20. Huw has a maths test.
(a)
For the first question, Huw divides 752 by a whole number.
His answer, which is correct, is 25 remainder 27.
What whole number did Huw divide by? [3]
(b)
The second question is:
| The only food provided for guests at Seaview Hotel is breakfast. The hotel has enough food to make breakfast for 20 guests for 6 days. How long would the food last 30 guests? You may assume each guest eats the same amount of food for breakfast. |
Here is Huw’s working.
| 20 guests | for | 6 days |
| 10 guests | for | 3 days |
| 30 guests | for | 9 days |
(i) Without working out the correct answer, explain why Huw’s answer of 9 days is incorrect. [1]
(ii) Work out the correct answer. [2]
| Scheme | Marks | Comments |
|---|---|---|
| (752 – 27 =) 725 | B1 | |
| 725 ÷ 25 | M1 | FT ‘their 752 – 27’ |
| 29 | A1 |
Alternative
Alternative method 1:
| Scheme | Marks | Comments |
|---|---|---|
| 752 ÷ 25 si | M1 | |
| 30 remainder 2 or 30.08 | A1 | |
| 29 | A1 |
Alternative method 2:
| Scheme | Marks | Comments |
|---|---|---|
| At least two trials of 25 × n or 752 ÷ n, where n is greater than 20 | M1 | |
| 25 × 29 = 725 | A1 | implies M1 |
| 29 | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| (i) Valid explanation e.g. ‘There are more guests so the food should not last longer.’ or ‘He has halved instead of doubling.’ or ‘The food will last for less time if there are more people.’ | E1 | ‘It is impossible’ without further explanation is E0 Allow e.g. ‘If you divide one side you have to multiply the other,’ Do not allow e.g. ‘You have to multiply not divide.’ (too vague) |
| (ii) 4 (days) | B2 | B1 for a correct intermediate step e.g. 10 guests and 12 days or for \(\dfrac{20 \times 6}{30}\) oe si |
| (6) |