A medium question on sum and multiple for P4–P5, with a step-by-step solution, diagrams and the answer. Sum-and-multiple and difference-and-multiple questions appear in the Hua Xia Cup's P3 to P5 first rounds, qualifying rounds and finals.
The question
Two brothers have 27 stickers between them.
After the older one gives the younger 8, the older has exactly twice as many as the younger.
How many did the older brother have at first?
Show the hints (2)
💡Hint 1: Does giving change the total?
💡Hint 2: After the gift, call the younger one part; the older is 2 parts. Find what each has after the gift first.
Worked solution
Have a go first, then read the solution step by step.
1.Giving doesn't change the total: still 27. After the gift the younger is 1 part and the older 2 parts: 3 parts in all.
2.1 part = 27 ÷ 3 = 9. After the gift: the younger has 9, the older 9 × 2 = 18.
3.Before the gift, those 8 were still the older one's: he had 18 + 8 = 26.
⚠️Common mistake: applying "2 times" to the starting numbers. It's true only after the gift.
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