Higher November 2024 Paper 3 Q5
5 Robyn buys a total of 240 pens and pencils, where
number of pens : number of pencils = 3 : 5
Robyn pays 9p for each pen.
She sells each pen for 11p.
Robyn pays 6p for each pencil.
She sells each pencil for 10p.
Robyn sells all of the pens and pencils.
Work out Robyn’s percentage profit.
Give your answer correct to 1 decimal place.
You must show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 45.6 | P1 | for a process to start to work with the ratio, eg \(240 \div (3 + 5)\ (= 30)\) or pens \(= 3n\) and pencils \(= 5n\) where \(n\) is a positive integer |
| P1 | for a complete process to find the number of pens and pencils, eg \(\text{``}30\text{''} \times 3\ (= 90)\) and \(\text{``}30\text{''} \times 5\ (= 150)\) OR for process to find one cost or amount to sell for one item eg \([\text{pens}] \times 9\ (= 810)\) or \([\text{pens}] \times 11\ (= 990)\) or \([\text{pencils}] \times 6\ (= 900)\) or \([\text{pencils}] \times 10\ (= 1500)\) OR process to find the profit for one pen or one pencil eg \(11 - 9\ (= 2)\) or \(10 - 6\ (= 4)\) | |
| P1 | for a process to find the total cost to buy or the total amount to sell for both, eg \([\text{pens}] \times 9 + [\text{pencils}] \times 6\ (= 1710)\) or \([\text{pens}] \times 11 + [\text{pencils}] \times 10\ (= 2490)\) OR process to find the profit for one item eg \([\text{pens}] \times 11 - [\text{pens}] \times 9\ (= 180)\) or \([\text{pens}] \times (11 - 9)\ (= 180)\) or \([\text{pencils}] \times 10 - [\text{pencils}] \times 6\ (= 600)\) or \([\text{pencils}] \times (10 - 6)\ (= 600)\) | |
| P1 | for a complete process to find the profit as a percentage or a decimal, eg \(\dfrac{[2490] - [1710]}{[1710]} \times 100\) or \(\dfrac{[2490] - [1710]}{[1710]}\ (= 0.456\ldots)\) or for a process to find the amount to sell as a percentage of the cost eg \(\dfrac{[2490]}{[1710]} \times 100\ (= 145.6\ldots)\) | |
| A1 | answer in the range 45.6 to 45.62 |
Additional guidance
Can work in £ or pence but must be consistent, 90 or 150 imply P1
This mark can be awarded at any stage
[pens] could be \(\text{``}30\text{''} \times 3\) or their number of pens
[pencils] could be \(\text{``}30\text{''} \times 5\) or their number of pencils
[pens], [pencils] \(\neq 1\)
180 or 600 or 780 implies P3
[2490] is their amount to sell for both pens and pencils
[1710] is their cost of pens and pencils
[2490] – [1710] may be [180] + [600]
If an answer is given in the range in working and then rounded incorrectly award full marks.
A correct answer with no supportive working gets 0 marks