Unit 7 · Finding Procedures
92 People on a Trip — How Many Minibuses?
Lesson 2 of 4
92 people, 2 large buses of 17, small buses of 8 for the rest. Three steps: subtract to find leftover people, divide by 8, round UP (you can't leave anyone behind), then add the 2 large buses back.
Transport and packaging problems requiring 'division with ceiling rounding' appear regularly in NSW Selective MR. The key move is rounding the quotient UP to the next whole number whenever there is any remainder — even a remainder of 1 requires a full extra bus.
The examiner tests whether students (a) correctly subtract 2 × 17 = 34 from 92 to get 58 remaining people; (b) divide 58 ÷ 8 = 7.25 and round UP to 8 small buses; and (c) add 2 + 8 = 10 total buses. The trap answer C (9) comes from forgetting to round up (using 7 small buses).
A group of people must be transported in two types of vehicles with different capacities. Some people fill the large vehicles first; the rest go in small vehicles. Since you can't have a fraction of a bus, any remainder requires an extra vehicle.
Best approach: Step 1: People in large vehicles = 2 × 17 = 34. Step 2: Remaining = 92 − 34 = 58. Step 3: Small buses = ⌈58 ÷ 8⌉ = ⌈7.25⌉ = 8. Step 4: Total = 2 + 8 = 10.
Question
92 people are going on a trip.
First they will fill two large minibuses, each with space for 17 people.
The rest of the people will travel in small minibuses, each with space for 8 people.
How many minibuses do they need in total?
Select an answer to see the explanation.
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