Linear Graphs & Gradients: WJEC GCSE Numeracy Higher November 2020 Unit 1 Q5

Numeracy Higher November 2020 Unit 1 Q5

WJECHigherCurrent spec6 marksLinear Graphs & Gradients

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.

Straight line graph of Overall cost (£), 0 to 1000, against Number of people, 0 to 300, from (0, 100) to (250, 1000)

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]

Mark scheme (a)

Scheme	Marks	Comments
(280 – 100 + 500) ÷ 50 or (280 – 100) ÷ 50 + 500 ÷ 50	M2	M1 for sight of any one of the following: (280 + 500) ÷ 50 (= £15.60) (280 – 100) ÷ 50 (= £3.60) (– 100 + 500) ÷ 50 (= £8)
(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: an answer of (£)680 (from 280 – 100 + 500) sight of 500 ÷ 50 correctly evaluated as (£)10, allow if embedded within other calculation

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: (1000 – 100) ÷ 250 (= £3.60) (460 -100) ÷ 100 (= £3.60) (640 -100) ÷ 150 (= £3.60) \(\dfrac{\text{‘an overall cost’} - 100}{\text{‘number of people for that overall cost’}}\) 1000 ÷ 250 + 500 ÷ 50 (= £14) 460 ÷ 100 + 500 ÷ 50 (= £14.60) 640 ÷ 150 + 500 ÷ 50 (= £ 14.26 or £14.27) \(\dfrac{\text{‘an overall cost’}}{\text{‘number of people for that overall cost’}}\) + \(\dfrac{500}{50}\)
(£) 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

Mark scheme (b)

Scheme	Marks	Comments
Considering a factor of 400 (200, 100 or 50) people or other suitable point, excluding £500 for charity, e.g. \(\dfrac{\text{‘an overall cost’} - 100}{\text{‘number of people for that overall cost’}}\) (200 people) (820 – 100) ÷ 200, (100 people) (460 – 100) ÷ 100, (50 people) (280 – 100) ÷ 50	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. (820 ÷ 200 + 1.25 = £) 5.35 (460 ÷ 100 + 1.25 = £) 5.85 (280 ÷ 50 + 1.25 = £) 6.85 correctly evaluated \(\dfrac{\text{‘an overall cost’}}{\text{‘number of people for that overall cost’}}\) + 1.25

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