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Maths olympiad question · P2–P3★ Easy

Working backwards: olympiad question 1

An easy question on working backwards for P2–P3, with a step-by-step solution, diagrams and the answer. Working-backwards questions appear in the Hua Xia Cup's P1 to P5 first rounds, qualifying rounds and finals.

The question

Ming had some sweets.

He ate 3, then Mum gave him 4 more.

Now he has 5.

How many sweets did Ming have at first?

Show the hints (2)
  1. Hint 1: Work backwards: how many did he have before Mum gave him some?
  2. Hint 2: Going backwards, “given” becomes “taken away” and “ate” becomes “put back”.

Worked solution

Have a go first, then read the solution step by step.

  1. 1.Before Mum's sweets: 5 − 4 = 1.
  2. 2.Before eating: 1 + 3 = 4.
  3. ⚠️Common mistake: still taking away what he ate and adding what he was given, which gives 6.

Answer: 4 sweets

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