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
At Chinese New Year two sisters got $218 in red-packet money altogether.
The older sister got $38 more than twice what the younger got.
How much did the older sister get?
Show the hints (2)
💡Hint 1: Without her extra $38, the older would have exactly twice as much. What would the total be then?
💡Hint 2: Then the younger is 1 part and the older 2 parts.
Worked solution
Have a go first, then read the solution step by step.
1.Call the younger's money 1 part: the older has 2 parts plus $38. Together they have $218.
2.Take away the older's extra $38 and she has exactly 2 parts: 218 − 38 = 180.
3.That is 3 parts, so the younger has 180 ÷ 3 = $60.
4.The older has 218 − 60 = $158.
⚠️Common mistake: adding the $38. The older has $38 extra, so take it away first.
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