Numeracy Higher June 2017 Unit 1 Q8
8. On a new housing estate, teams of painters paint the walls and ceilings of houses once they are built.
It takes a team of 5 painters 10 hours to paint a house that has a total wall and ceiling area of 500 m2.
A new house on the estate has a total wall and ceiling area of 600 m2.
This house has to be painted in 8 hours.
Calculate the least number of painters needed.
You must show all your working. [4]
| Scheme | Marks | Comments | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| M1 | |||||||||||||||
| 600/80 OR 60/8 | M1 | May be implied. This M1 implies the previous M1 | ||||||||||||||
| = 7·5 or equivalent | A1 | CAO. May not be seen. | ||||||||||||||
| = 8 (painters) | A1 | FT provided at least M1 awarded and rounding required A correct answer of 8 (with no errors) from M1 awarded gains all 4 marks |
Alternative methods
M1 for n painters take 1 hour to paint 10n (m2)
M1 for 600/8
A1 for 75 (m2 / hour)
A1 for 8 (painters)
A correct answer of 8 (with no errors) from M1 awarded gains all 4 marks
OR
M2 for \(5 \times \dfrac{10}{8} \times \dfrac{600}{500}\)
This is for the correct use of the 5 with all 4 numbers, 10, 8, 600 and 500
M1 for correct use of the 5 with any 2 of the numbers
A1 for 7·5 or equivalent. CAO. May not be seen
A1 for 8 (painters)
FT provided at least M1 awarded and rounding required
A correct answer of 8 (with no errors) from M1 awarded gains all 4 marks
| Scheme | Marks | Comments |
|---|---|---|
| Valid assumption e.g. 'All painters work at the same rate (or speed)', ‘They all paint 10(m2) in an hour’ ‘Each painter is equally efficient’ | B1 | Do not accept e.g. ‘The rooms (or walls) are the same shape’, ‘They had the same breaks’ ‘They don’t have breaks’ ‘Each painter works at a constant speed’ |