This question is based on your work on M U123 up to and including Unit 7. Jude is organising a retirement party for his partner. He has found two suitable local venues which can accommodate his needs. The local hotel charges 1'15 per person for a buffet and 425 for a large room with a bar. A local pub charges 18 per person for a buffet with a similar room costing 320. (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 20 30 45 The local hotel 1100 The local pub 1130 (b) For the local hotel, the linear equation 3/ : 151: + 425 can be used to model the total cost y (in pounds) for a: people attending. (0 Explain how this equation is constructed to show that it holds. (ii) Write down a similar equation that can be used to model the total (C) (i) (ii) cost y (in pounds) for a: people attending the local pub. Using the same axes, draw graphs of the two equations from part (b). Use an :r-scale from 0 to 45, 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 hour to use Graphplotter if you are having di'lcultg adjusting the limits for the slope and intercept (1) What do the gradients of these lines represent in terms of the situation being modelled? (2) What do the yintercepts 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) Jude nds out that 42 people are going to attend. The local pub offers a discount of 5% per person off the price of the buffet when the number of people attending is greater than 40. Should this affect Jude's choice of venue for the party? Justify your answer. [2'] [1]