5. Petra is organising a prom for her year group. The number of people attending the prom is likely to be between 20 and 80.
The cost of holding the prom at Hotel Afonwen would be as follows.
Hire of the room: £100
Food: £15 per person
Welcome drink on arrival: £3 per person
Decorations: £2 per person
(a)
Draw a graph to illustrate the total cost of holding the prom for between 20 and 80 people. Use the graph paper below. [4]
(b)
Petra decides to share all the costs equally between the people attending.
Let £P be the price paid per person.
Let N be the number of people attending the prom.
Write a formula for P, in terms of N. [3]
(c)
Hiring a larger room at Hotel Afonwen costs £200. The cost per person for food, welcome drinks and decorations remains the same. If the total cost is £2240, how many people attend? [2]
Mark scheme (a)
Scheme
Marks
Comments
Axes labelled appropriately, e.g. (total) cost and (number of) people, AND uniform number of people scale from 20 (or less) to at least 80
B1
Allow people and costs on either axis Allow ‘£’ for costs
Reasonable uniform total cost scale from 500 (or less) to at least 1700
B1
Correct representation of the total cost for between 20 and 80 people
B2
People
20
40
60
80
Cost £
500
900
1300
1700
FT 'their scale' if possible Ignore showing for less than 20 people (and up to 100 people) May be indicated by an appropriate straight line from 20 to 80 people (£500 to £1700) B1 for any 2 correct points given (indicated in working or plotted) OR B1 for all points (indicated in working or plotted), within the range 20 to 80 people inclusive, with a gradient of 20
Mark scheme (b)
Scheme
Marks
Comments
\(P = 20 + \dfrac{100}{N}\) or equivalent
B3
Mark final answer B2 for 20 + 100/N or P = … + 100/N B1 for sight of 100/N
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