Today’s problem — free all day, every step. Every day has one.
Bus passengers — boarding, alighting, doubling
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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65 worked examples are free without a code, two from every pattern. No account, either way.
The pattern behind it: Working backwards
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.
How to spot it
The question gives the final amount after a sequence of changes and asks what the amount was 'at first' or 'to begin with'.
Common mistake
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%.
Try one like it
Standard Cable car — passengers double at the second station There were some passengers in a cable car. At the first station, 15 passengers boarded and 6 got off. At the second station, the n…The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.