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Question 3(a)3t = (7k/13) – 173t + 17 = (7k/13) – 17 + 17 (By adding 17 on both sides)3t + 17 = (7k/13)(3t+17)(13/7) =(7k/13)(13/7) (By multiplying 13/7 on both sides)Hence, k = (13/7) (3t+17)(b)7k = (4k/3t) – 11t7k + 11t = (4k/3t) – 11t + 11t (Adding 11t on both sides)7k + 11t = (4k/3t)Taking 7k to the RHS, we get11t = (4k/3t) – 7k11t = k [(4/3t) – 7] (Taking k common on RHS)Hence, k = 11t[(4/3t) – 7]Thus, k = (44/3)t2– 77tQuestion 4(a)Number of teenagers = 26Computation of Cinema CostsCinema charges = 4*26 = £104Transport charges to cinema = £90Hence, total cinema cost = 104+ 90 = £194Computation of bowling costsBowling alley charges = 5.5*26 = £143Transport charges to bowling = £45Hence, total bowling costs = 143 + 45 = £188
Number of teenagers = 38Computation of Cinema CostsCinema charges = 4*38 = £152Transport charges to cinema = £90Hence, total cinema cost = 152+ 90 = £242Computation of bowling costsBowling alley charges = 5.5*38= £209Transport charges to bowling = £45Hence, total bowling costs = 209 + 45 = £254(b)For the cinema charges, the relevant equation is given as y = 4x + 90The above equation holds since £90 is a fixed transportation cost for the group and isindependent of the number of teenagers. Further, the cost of cinema per teenager is £4 andhence, the variable cost would be 4x where x is the number of teenagers.With regards to bowling, fixed transport charges are £45. Also, per teenager cost for bowlingalley is £5.5.Hence, y = 5.5x + 45(c ) (i) The relevant costs are captured in the table below.The relevant graph is indicated below.