A medium question on surplus and shortage for P3–P4, with a step-by-step solution, diagrams and the answer. Surplus-and-shortage questions appear in the Hua Xia Cup's P1 to P5 papers; harder ones become questions about distance and time.
The question
A class is chipping in for a present for their teacher, everyone paying the same.
At $6 each they are $102 short; at $8 each they are still $56 short.
How much does the present cost?
Show the hints (2)
💡Hint 1: Going from $6 each to $8 each, how much smaller does the shortfall get?
💡Hint 2: Find how many pupils there are first, then the price.
Worked solution
Have a go first, then read the solution step by step.
1.At $6 each they are $102 short.
2.At $8 each, everyone pays $8 − $6 = $2 more, and they are still $56 short.
3.The shortfall drops from $102 to $56: 102 − 56 = $46, which is what everyone paid more in all.
4.At $2 more each, there are 46 ÷ 2 = 23 pupils.
5.Price: 23 × $6 + $102 = $240.
⚠️Common mistake: adding 102 + 56. Both times they are short, so subtract.
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