A hard question on sum and difference for P4–P5, 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 bakery has a main shop and a branch, with 507 boxes of mooncakes between them.
After the main shop sends 33 boxes to the branch, the branch has 5 boxes more than the main shop.
How many boxes did the main shop have at first?
Show the hints (3)
💡Hint 1: Does sending boxes change the total?
💡Hint 2: After the move there are 507 boxes in all and the branch has 5 more. How many does the main shop have then?
💡Hint 3: After the move, the main shop has 251. Now think back to before.
Worked solution
Have a go first, then read the solution step by step.
1.Before and after the move the total is 507. After it, the branch has 5 more than the main shop.
2.Take away the branch's 5 extra and the two are equal: the main shop has (507 − 5) ÷ 2 = 251, the branch 251 + 5 = 256.
3.Before the move, those 33 boxes were still at the main shop: it had 251 + 33 = 284.
4.Check: the branch had 507 − 284 = 223; 223 + 33 = 256, which is 5 more than 251 ✓
⚠️Common mistake: using (507 + 5) ÷ 2 or (507 − 5) ÷ 2 as the starting number. The gap of 5 is after the move, not before.
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