A medium question on sum and difference for P2–P4, 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
A bookcase in the school library has three shelves holding 74 books in all.
The top shelf has 4 more than the middle one, and the middle one has 2 more than the bottom one.
How many books are on the bottom shelf?
Show the hints (2)
💡Hint 1: Which shelf has the fewest? How many more does each of the others have?
💡Hint 2: Take away the extra books on the top and middle shelves, and all three are equal. How many do you take away?
Worked solution
Have a go first, then read the solution step by step.
1.Start from the bottom shelf, the smallest: the middle has 2 more; the top has 4 more than the middle, so 4 + 2 = 6 more than the bottom.
2.Take the extras away: 74 − 2 − 6 = 66, and now all three are equal.
3.All three equal: the bottom shelf has 66 ÷ 3 = 22.
⚠️Common mistake: taking away only 4 + 2. The top has 6 more than the bottom, not 4.
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