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Marbles — a magic trick doubles the jar
Ravi had some marbles in a jar. He added 20 marbles and removed 8 marbles. Then a magic trick doubled the number of marbles in the jar. There were then 70 marbles. How many marbles were in the jar before he added or removed any?
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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 in reverse order, using the opposite operation each time: undo the doubling first, then undo the net gain.
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 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 pas…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.
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