An expert question on sum and difference for P5–P6, 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 cha chaan teng, every milk tea costs the same, as does every pineapple bun with butter and every French toast.
One French toast is $2 cheaper than a milk tea and a pineapple bun together.
3 milk teas cost $28 more than 2 pineapple buns.
A family ordered 2 plates of French toast, 4 milk teas and 4 pineapple buns, and paid $182.
How much is one French toast?
Show the hints (3)
💡Hint 1: Use the first fact: think of each French toast as a milk tea plus a pineapple bun.
💡Hint 2: After that, the bill's 6 milk teas can be swapped for pineapple buns with the second fact, leaving only buns.
💡Hint 3: A pineapple bun is $13 and a milk tea $18.
Worked solution
Have a go first, then read the solution step by step.
1.From the first fact: 1 French toast = 1 milk tea + 1 bun − $2, so 2 plates of French toast = 2 milk teas + 2 buns − $4.
2.Swap the French toast on the bill: 6 milk teas + 6 buns − $4 = $182, i.e. 6 milk teas + 6 buns = $182 + $4 = $186.
3.From the second fact: 3 milk teas = 2 buns + $28, so 6 milk teas = 4 buns + $56.
4.Swap the 6 milk teas for buns too: 10 buns + $56 = $186, so 10 buns = $186 − $56 = $130, and one bun is $130 ÷ 10 = $13.
5.3 milk teas = 2 × 13 + 28 = $54, so one is $18.
6.One French toast = $18 + $13 − $2 = $29.
7.Check: 2 × 29 + 4 × 18 + 4 × 13 = 182 ✓
⚠️Common mistake: swapping the French toast without taking off $2 a plate — $4 in all.
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