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
At a bakery every pineapple bun costs the same, and so does every cocktail bun.
3 pineapple buns cost $28 more than 2 cocktail buns;
3 cocktail buns cost $3 more than 2 pineapple buns.
How much is one pineapple bun?
Show the hints (3)
💡Hint 1: Try adding the two facts together. How many of each are left?
💡Hint 2: Then subtract one fact from the other to find how much dearer one pineapple bun is than one cocktail bun.
💡Hint 3: One of each costs $31 together, and the pineapple bun is $5 dearer.
Worked solution
Have a go first, then read the solution step by step.
1.Draw the two facts as bars: 3 pineapple buns = 2 cocktail buns + $28; 3 cocktail buns = 2 pineapple buns + $3.
2.Add them: 3 of each = 2 of each + $28 + $3. Take 2 of each away from both sides: one of each costs $28 + $3 = $31.
3.Now put them together another way: 3 pineapple buns = 2 cocktail buns + $28, and 2 pineapple buns = 3 cocktail buns − $3. Together, 5 pineapple buns = 5 cocktail buns + $28 − $3 = 5 cocktail buns + $25.
4.Pair the 5 pineapple buns with the 5 cocktail buns: each pineapple bun is $25 ÷ 5 = $5 dearer than a cocktail bun.
5.One of each costs $31, and the pineapple bun is $5 dearer: one pineapple bun = ($31 + $5) ÷ 2 = $18.
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