An easy question on sum and multiple for P3–P4, 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
There are pigeons and sparrows on the grass in the park.
There are 3 times as many pigeons as sparrows, and 10 more pigeons than sparrows.
How many sparrows are there?
Show the hints (2)
💡Hint 1: Call the sparrows 1 part. How many more parts are the pigeons?
💡Hint 2: Those extra parts are the 10 extra.
Worked solution
Have a go first, then read the solution step by step.
1.The pigeons are 3 parts and the sparrows 1 part: 3 − 1 = 2 parts more.
2.Those 2 parts are the 10 extra, so 1 part = 10 ÷ 2 = 5: 5 sparrows.
⚠️Common mistake: 10 ÷ 3. The extra is 2 parts, not 3.
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