Today’s problem — free all day, every step. Every day has one.
Shuttle bus — tourists on and off at two stops
A shuttle bus left the airport carrying some tourists. At the first station, of the tourists in it alighted and 5 tourists boarded it. At the second station, of the tourists in it alighted and 11 tourists boarded the bus. When it left the second station, there were 30 tourists in it. How many tourists were there in the bus when it left the airport?
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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 from the end, undoing each event in reverse order — which means at each stop you undo the boarding before the alighting, because forwards the alighting happened first.
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 Ivan and Helen — half his money Ivan gave half of his money to Helen. He then spent $18 and was left with $12. How much money did Ivan have at first?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.