Question P3–P4–P5–P6 Working backwards
Today’s problem — free all day, every step. Every day has one.
There were some passengers on a bus. At the first stop, 12 passengers boarded and 5 got off. At the second stop, the number of passengers doubled. There were then 42 passengers. How many passengers were on the bus before the first stop?
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You know how it ended. Undo each step, last one first.
In this one. Work backwards, undoing the last operation first: halve 42 to get 21, then take off the net gain of 7.
The question gives the final amount after a sequence of changes and asks what the amount was 'at first' or 'to begin with'.
Children undo the steps in the same order they happened rather than in reverse, or forget that a percentage profit is added to the cost price, so the final price is 120% of it, not 100%.
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