Today’s problem — free all day, every step. Every day has one.
A tank of oil — morning and afternoon
A mechanic had a tank of oil. He used half of it to service cars in the morning. In the afternoon he used a further 3.5 litres and was left with 2.5 litres. How many litres of oil did the tank hold at first?
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The pattern behind it: Working backwards
You know how it ended. Undo each step, last one first.
In this one. Work backwards: rebuild the half kept after the morning from the afternoon use and the amount left, then double that half to recover the whole tank.
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%.
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.