Numeracy Foundation November 2016 Unit 2 Q5
5. Dafydd plans to hire a van.
He can only hire the van for a whole number of days.
The cost of hiring the van is given by the formula:
hire cost = £42 × number of days + booking fee
(a) Circle either TRUE or FALSE for each of the following statements. [2]
| When the booking fee is £18, the hire cost for 2 days is £102. | TRUE | FALSE |
| The hire cost is always greater than the booking fee. | TRUE | FALSE |
| When the van is hired for one extra day, the hire cost will be an extra £42. | TRUE | FALSE |
| The hire cost for 2 days is double the hire cost for 1 day. | TRUE | FALSE |
(b) Explain why the hire cost cannot be £124 when the booking fee is £18.
You must show all your working. [2]
You must show all your working. [2]
| Scheme | Marks | Comments |
|---|---|---|
| True True True False | B2 | B1 for any three correct. |
| Scheme | Marks | Comments |
|---|---|---|
| Engaging in appropriate calculations using the formula, sufficient to draw a conclusion. e.g. Hire cost for 2 days = £102 AND hire cost for 3 days = £144. | B1 | The working and the explanation need to be considered together for the award of B1 E1. OR e.g. Hire cost for 2 days = (£)102 Each extra day costs £42 (£124) is only (£)22 more and so is not enough for an extra day. |
| Appropriate explanation e.g.£124 is between £102 and £144 so the number of days is between 2 and 3 so it is not a whole number | E1 |
Alternative:
| Scheme | Marks | Comments |
|---|---|---|
| Number of days = (124 − 18) /42 (=2·5238095…) | B1 | |
| The number of days must be a whole number so the number of days cannot be a decimal | E1 |
Alternative:
| Scheme | Marks | Comments |
|---|---|---|
| 124 – 18 = (£)106 106 – 42 – 42 = (£22) | B1 | |
| (£) 22 is not enough for another day. | E1 |