Question 4 – 20 marks This question is based on your work on MU123 up to and including Unit 7. Neil is organising an out
Posted: Mon May 09, 2022 1:38 pm
Question 4 – 20 marks This question is based on your work on
MU123 up to and including Unit 7. Neil is organising an outdoor
adventure trip for a group of teenagers from his local youth group
where he is an adult volunteer. He has two options, which both
offer packages for groups of up to 30. Option A charges £15 per
teenager and a non-refundable booking fee of £220. Option B charges
£24 per teenager and a non-refundable booking fee of £40. (a) Copy
and complete Table 1 by working out how much it costs to go to each
option for the numbers of teenagers attending shown. Table 1 Total
cost in pounds for each option Number of teenagers attending 18 24
30 Option A 670 Option B 760 [2] (b) The linear equation y = 15x +
220 can be used to model the total cost y (in pounds) for x
teenagers attending Option A. (i) Explain how the equation is
constructed in order to show that it holds. [1] (ii) Write down a
similar equation that can be used to model the total cost y (in
pounds) for x teenagers attending Option B. [1] (c) (i) Using the
same axes, draw graphs of the two equations from part (b). Use an
x-scale from 0 to 30, and choose a y-scale that allows both lines
to be seen over this range. You may draw your graphs by hand, using
squared paper, or use Graphplotter. Remember to label the lines
with their equations. See the screencast on how to use Graphplotter
if you are having difficulty adjusting the limits for the slope and
intercept. Include your graphs with the rest of your TMA [4] (ii)
(1) What do the gradients of these lines represent in terms of the
situation being modelled? [1] (2) What do the y-intercepts of these
lines represent in terms of the situation being modelled? [1] (d)
The lines representing the equations in part (b) intersect. Use
your graphs to write down the approximate coordinates of the
intersection point. How can the intersection point be interpreted
in this model? [2] (e) Use algebra to solve the two simultaneous
equations from part (b). Show each step of your working clearly.
[4] (f) State which option gives the better deal, in terms of cost,
for different numbers attending. [2] (g) Neil finds out that 26
teenagers are going to attend. If Option B offers a discount of 10%
per teenager off the entry price when the group size is greater
than 25, which venue should Neil choose for the outdoor adventure
trip, taking the changes in pricing into account? Justify your
ans
MU123 up to and including Unit 7. Neil is organising an outdoor
adventure trip for a group of teenagers from his local youth group
where he is an adult volunteer. He has two options, which both
offer packages for groups of up to 30. Option A charges £15 per
teenager and a non-refundable booking fee of £220. Option B charges
£24 per teenager and a non-refundable booking fee of £40. (a) Copy
and complete Table 1 by working out how much it costs to go to each
option for the numbers of teenagers attending shown. Table 1 Total
cost in pounds for each option Number of teenagers attending 18 24
30 Option A 670 Option B 760 [2] (b) The linear equation y = 15x +
220 can be used to model the total cost y (in pounds) for x
teenagers attending Option A. (i) Explain how the equation is
constructed in order to show that it holds. [1] (ii) Write down a
similar equation that can be used to model the total cost y (in
pounds) for x teenagers attending Option B. [1] (c) (i) Using the
same axes, draw graphs of the two equations from part (b). Use an
x-scale from 0 to 30, and choose a y-scale that allows both lines
to be seen over this range. You may draw your graphs by hand, using
squared paper, or use Graphplotter. Remember to label the lines
with their equations. See the screencast on how to use Graphplotter
if you are having difficulty adjusting the limits for the slope and
intercept. Include your graphs with the rest of your TMA [4] (ii)
(1) What do the gradients of these lines represent in terms of the
situation being modelled? [1] (2) What do the y-intercepts of these
lines represent in terms of the situation being modelled? [1] (d)
The lines representing the equations in part (b) intersect. Use
your graphs to write down the approximate coordinates of the
intersection point. How can the intersection point be interpreted
in this model? [2] (e) Use algebra to solve the two simultaneous
equations from part (b). Show each step of your working clearly.
[4] (f) State which option gives the better deal, in terms of cost,
for different numbers attending. [2] (g) Neil finds out that 26
teenagers are going to attend. If Option B offers a discount of 10%
per teenager off the entry price when the group size is greater
than 25, which venue should Neil choose for the outdoor adventure
trip, taking the changes in pricing into account? Justify your
ans