Two competing bus companies offer weekly travel passes to commuters in the same town. Company A charges \(A = 3j + 8\) and Company B charges \(B = 2j + 15\)...
Question 1 Report
Two competing bus companies offer weekly travel passes to commuters in the same town. Company A charges \(A = 3j + 8\) and Company B charges \(B = 2j + 15\), where \(j\) is the number of journeys made that week, both in pounds.
- Work out the cost with Company A for 12 journeys. (2)
- Find the value of \(j\) for which both companies charge the same amount. (2)
- State, with a reason, which company is cheaper for a passenger who makes 20 journeys in a week. (2)
Answer Details
(a) Substituting \(j = 12\) into \(A = 3j + 8\) gives \(A = 3(12) + 8 = 36 + 8 = 44\) pounds [2 marks].
(b) The two companies charge the same amount when \(A = B\), so \(3j + 8 = 2j + 15\). Subtracting \(2j\) and 8 from both sides gives \(j = 7\) [2 marks].
(c) Substituting \(j = 20\) into each formula gives \(A = 3(20) + 8 = 68\) and \(B = 2(20) + 15 = 55\). Since 55 is less than 68, Company B is cheaper for 20 journeys in a week [2 marks]. This makes sense because Company B has a lower rate per journey, so it becomes relatively cheaper the more journeys are made, even though its fixed charge is higher.
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