Science-Fair Transport: Buses, Discounts and Budget
Grade 11 at Thuso High is planning a science-fair trip to Maseru, 240 km away. There are 186 learners and 12 teachers; every bus must carry at least one teacher. Company A offers 56-seater buses at M9,800 per bus plus M1.85 per kilometre per bus. Company B offers 64-seater buses at M11,200 per bus plus M2.10 per kilometre per bus. The school has M78,000 for transport and must reserve M4,500 for emergencies. A parent has offered a 12% discount on the total hire cost if the school books Company B before Friday. The trip coordinator wants to seat everyone comfortably, keep at least two empty seats on each bus for luggage, and stay within the transport budget after the emergency reserve. She also needs to know the transport cost per learner if teachers travel free.
1. Determine the minimum number of buses needed from each company, respecting the teacher and empty-seat constraints. Show the seating check.
Read the worked answer
Total travellers = 186 + 12 = 198. For Company A, 3 buses give 3 × 56 = 168 seats, too few. Four buses give 224 seats, but with at least two empty seats per bus the usable seats are 4 × (56 − 2) = 216, which is ≥ 198. So A needs 4 buses. For Company B, 3 buses give 192 seats, already below 198, so 3 is impossible. Four buses give 256 seats; usable seats = 4 × (64 − 2) = 248 ≥ 198. So B also needs 4 buses. The teacher rule is satisfied because 12 teachers can be distributed with at least one per bus (for example 3, 3, 3, 3).
2. Calculate the total transport cost for each company, including the 12% discount for Company B, and state whether the school stays within the M78,000 budget after reserving M4,500.
Read the worked answer
Available for transport = 78,000 − 4,500 = M73,500. Company A: distance charge per bus = 1.85 × 240 = M444; cost per bus = 9,800 + 444 = M10,244; total = 4 × 10,244 = M40,976. Company B before discount: distance charge = 2.10 × 240 = M504; cost per bus = 11,200 + 504 = M11,704; total = 4 × 11,704 = M46,816. Discount = 12%, so pay 88%: 0.88 × 46,816 = M41,198.08. Both totals are below M73,500, so the school stays within budget. Company A is cheaper by 41,198.08 − 40,976 = M222.08.
3. Find the transport cost per learner if teachers travel free, for each company, and recommend which booking is better. Give one non-cost reason that could change the decision.
Read the worked answer
Teachers travel free, so the cost is shared by 186 learners. Company A: 40,976 ÷ 186 = M220.30 per learner (2 d.p.). Company B: 41,198.08 ÷ 186 = M221.50 per learner. Company A is lower by about M1.20 per learner and also has the lower total cost, so on cost grounds book A. A non-cost reason could change the decision: Company B’s 64-seat buses give more empty seats (58 unused before the luggage rule) and more comfort for a 240 km trip; or the 12% discount may depend on booking before Friday, so missing the deadline removes B’s advantage and makes A clearly cheaper. The coordinator should check reliability and cancellation terms before finalising.