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Question Working backwards

Working backwards

Sam and Jasmine had 480 stickers. After Sam gave away 50% of his stickers and Jasmine then gave 30% of hers to Sam, Sam had 270 stickers. How many did Jasmine have at first?

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About this method

Working backwards

You know how it ended. Undo each step, last one first.

In this one. Work backward by reversing what each percentage statement did: the 70% Jasmine kept reveals her amount before the transfer, then Sam's 50% kept reveals his starting amount.

What you are toldonly the endleft$12Undo the spendingput the $18 backbefore12 + 18 = 30Undo the givinghalf had gone to Helenat first30 doubled = 60

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%.

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