A medium question on sum and difference for P2–P4, with a step-by-step solution, diagrams and the answer. A regular in primary maths competitions such as the Hua Xia Cup, from the P1 and P2 first rounds to the P5 finals.
The question
A classroom has two bookcases, A and B, holding 54 books in all.
After 2 are moved from bookcase A to bookcase B, the two hold the same number.
How many books were in bookcase B at first?
Show the hints (2)
💡Hint 1: Does moving them change the total?
💡Hint 2: When they're equal, how many are in each? Then think back to before the move.
Worked solution
Have a go first, then read the solution step by step.
1.Moving them doesn't change the total. Afterwards the two are equal: 54 ÷ 2 = 27 each.
2.Before the move, B didn't have those 2 yet: B held 27 − 2 = 25 at first.
⚠️Common mistake: thinking they differed by 2. One lost 2 and the other gained 2, so they differed by 4.
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