An easy question on surplus and shortage for P2–P3, with a step-by-step solution, diagrams and the answer. Surplus-and-shortage questions appear in the Hua Xia Cup's P1 to P5 papers; harder ones become questions about distance and time.
The question
Mum shares a bag of sweets equally among some children.
With 2 each there are 5 left over; with 3 each they are used up exactly.
How many children are there?
Show the hints (2)
💡Hint 1: Going from 2 each to 3 each, how many more does each child get?
💡Hint 2: The 5 left over are just enough for that.
Worked solution
Have a go first, then read the solution step by step.
1.With 2 each, 5 are left over.
2.With 3 each, every child gets 3 − 2 = 1 more, which uses up the 5 left over exactly.
3.The 5 left over, 1 a child, go round 5 ÷ 1 = 5 children.
⚠️Common mistake: 5 ÷ 3. The leftovers only pay for 1 more each.
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