Numeracy Intermediate November 2017 Unit 1 Q6
6. Truetool is a tool hire company.
| Hire charges |
| The cost of hiring a cement mixer in £: 13 × number of days + 26 |
| The cost of hiring a jet washer in £: 9 × number of days + 38 |
(a) Sara hires a cement mixer for 5 days and a jet washer for 7 days from Truetool.
How much change would she get from £200? [3]
How much change would she get from £200? [3]
(b) Geraint hired a cement mixer for a number of days.
Lois hired a jet washer for the same number of days.
They each paid the same amount of money.
Lois hired a jet washer for the same number of days.
They each paid the same amount of money.
For how many days did they each hire these tools from Truetool?
You must show all your working. [3]
Number of days ……………
| Scheme | Marks | Comments |
|---|---|---|
| 5 × 13 + 26 + 9 × 7 + 38 ( 91 + 101) (£)192 | M1 A1 | Attempt to add must be implied, not for sight of 5 × 13 + 26 and 9 × 7 + 38 CAO If units are given they must be correct |
| (Change) (£) 8 | B1 | FT 200 - ‘their £192’ provided ≤ £200 and either
5 × 13 + 26 + 9 × 5 + 38 (= £174) or 7 × 13 + 26 + 9 × 7 + 38 (= £218) as misreads, however award of B1 may be possible |
| Scheme | Marks | Comments | |||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Equating 13x + 26 with 9x + 38 or sight of a correct evaluated trial of the same number of days for cement mixer and jet washer | B1 | Formal notation is not required Sight of 13x + 26 with 9x + 38 is insufficient without further correct working | |||||||||||||||||||||||||||
| 13x – 9x = 38 – 26 or 4x = 12 or x = 12/4 or trial & improvement (i.e. testing for a number of days with a 2nd trial getting closer to 3 days unless original trial is 3 days) | M1 | FT equivalent level of difficulty Method to solve may be informal | |||||||||||||||||||||||||||
| 3 (days) | A1 | CAO. Some relevant working must be seen to award all 3 marks Do not award all 3 marks for an unsupported correct response, however award SC2 Sight of both costing (£)65 is B1, M1, but A0 if 3 days not seen in working A final answer of 65 (days) is B1, M1, A0
|