Numeracy Higher November 2020 Unit 1 Q5
5. Meinir is planning a charity event to be held at a hotel.
A section of a straight line graph showing the hotel charges for this event is shown below.
These charges include a single payment for the room hire and the cost of one drink for each person attending.
Meinir decides to pay the room hire cost herself.
She decides to price the tickets so that she will be able to make £500 to give to charity.
(a) Calculate the selling price of each ticket if Meinir plans the event for 50 people. [3]
(b) Calculate the selling price of each ticket if Meinir plans the event for 400 people. [3]
| Scheme | Marks | Comments |
|---|---|---|
| (280 – 100 + 500) ÷ 50 or (280 – 100) ÷ 50 + 500 ÷ 50 | M2 | M1 for sight of any one of the following:
|
| (Sell each ticket for) (£) 13.6(0) | A1 | If units are given they must be correct FT from M1 awarded If no marks, award SC1 for either of the following:
|
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (1000 – 100) ÷ 250 + 500 ÷ 50 or equivalent using any two points on the line, e.g. (460 -100) ÷ 100 + 500 ÷ 50 (640 -100) ÷ 150 + 500 ÷ 50 | M2 | M1 for sight of any one of the following, or equivalent:
|
| (£) 13.6(0) | A1 | If units are given they must be correct FT from M1 awarded with answer rounded or truncated to a penny If no marks, award SC1 for sight of 500 ÷ 50 correctly evaluated as (£)10, allow if embedded within other calculation |
| Scheme | Marks | Comments |
|---|---|---|
Considering a factor of 400 (200, 100 or 50) people or other suitable point, excluding £500 for charity, e.g.
| M1 | FT ‘their \(\dfrac{\text{‘an overall cost’} - 100}{\text{‘number of people for that overall cost’}}\) ’ i.e. ‘their 3.60’ (= £3.60) |
| (Charity contribution) 500 ÷ 400 | M1 | (= £ 1.25) May be embedded within stages of calculation |
| (Total) (£) 4.85 | A1 | If units are given they must be correct If M0, M1, A0 also award SC1 for correct evaluation resulting from the omission of deducting £100, e.g.
|
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Considering total cost for 400 people, e.g. (400 ÷ 50) × (280–100) + 500 or 8 × 180 + 500 or 1440 + 500 or (400 ÷ 100) × (460–100) + 500 or 4 × 360 + 500 or (400 ÷ 200) × (820–100) + 500 or 2 × 720 + 500 or equivalent | M1 | |
| ÷ 400 | m1 | |
| (£) 4.85 | A1 | If units are given they must be correct If no marks (due to omission of £100), award SC1 for (8 × 280 + 500) ÷ 400 or SC2 for answer (£)6.85 or SC1 for (4 × 460 + 500) ÷ 400 or SC2 for answer (£)5.85 or SC1 for (2 × 820 + 500) ÷ 400 or SC2 for answer (£)5.35 |