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