A medium question on working backwards for P3–P4, with a step-by-step solution, diagrams and the answer. Working-backwards questions appear in the Hua Xia Cup's P1 to P5 first rounds, qualifying rounds and finals.
The question
A bus leaves the terminus.
At the first stop, half the passengers get off and then 4 get on.
At the second stop, half the passengers get off again and nobody gets on.
Now there are 10 passengers on board.
How many passengers were on the bus when it left the terminus?
Show the hints (2)
💡Hint 1: Work backwards: how many were on board before people got off at the second stop?
💡Hint 2: Going back: before "half get off" there were twice as many; before "4 get on" there were 4 fewer.
Worked solution
Have a go first, then read the solution step by step.
1.Before the second stop: 10 × 2 = 20.
2.Before people got on at the first stop: 20 − 4 = 16.
3.Before people got off at the first stop: 16 × 2 = 32.
⚠️Common mistake: forgetting that undoing "4 get on" means taking 4 away.
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