Question 3 5 marks This question is based on your work on MU123 up to and including Unit 7. Make k the subject of the following two equations. Show each step of your working. 11k (a) 5t = +7 4 4k (b) 7k = 5t + 91Question 4 - 20 marks This question is based on your work on MU123 up to and including Unit 7. Naomi is organising a trip to see a show for her local choir group. She is considering two options, which both offer packages for groups of up to 30. Option A charges $25 per person and a non-refundable booking fee of 230. Option B charges [20 per person and a non-refundable booking fee of 2120. (a) Copy and complete Table 1 by working out how much it costs to go to each option for the numbers of people attending shown. Table 1 Total cost in pounds for each option Number of people attending 15 25 30 Option A 780 Option B 720 (b) The linear equation y = 25r + 30 can be used to model the total cost y (in pounds) for r people attending Option A. (i) Explain how the equation is constructed in order to show that it holds. (ii) Write down a similar equation that can be used to model the total cost y (in pounds) for a people attending Option B. (c) (i) Using the same axes, draw graphs of the two equations from part (b). Use an r-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 using Graphplotter and include them with the rest of your TMA. 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. (ii) (1) What do the gradients of these lines represent in terms of the situation being modelled? (2) What do the y-intercepts of these lines represent in terms of the situation being modelled? (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? (e) Use algebra to solve the two simultaneous equations from part (b). Show each step of your working clearly. (f) State which option gives the better deal, in terms of cost, for different numbers attending. (g) Naomi finds out that 28 people are going to attend. Option A offers a discount of 10% off the per person entry price when the group size is greater than 25. Should this affect Naomi's choice of show? Justify your