At a food stall, Mr Tan nests identical reusable takeaway boxes. Each additional nested box raises the total height by the same amount. A stack of 5 boxes is 21 cm high, while a stack of 8 boxes is 27 cm high. The shelf has 50 cm of clear height.
- Find the extra height added to the stack by each additional box.
- What is the greatest number of boxes Mr Tan can stack on the shelf?
Need a hint?
Compare the change from 5 boxes to 8 boxes. Then remember that the bottom box is already present in both stacks.
Worked answer
- Going from 5 boxes to 8 boxes adds 3 boxes.
- The stack becomes 27 − 21 = 6 cm taller.
- Each additional box adds 6 ÷ 3 = 2 cm.
- There are 4 additions above the bottom box, so the bottom box is 21 − 4 × 2 = 13 cm high.
- A stack of n boxes has height 13 + (n − 1) × 2 cm.
- A stack of 19 boxes is 13 + 18 × 2 = 49 cm high.
- A stack of 20 boxes is 13 + 19 × 2 = 51 cm high, so 19 boxes is the greatest number that fits.
Answer: 19 boxes
The mistake this question tests
Habit
Calculation slip
A common mistake is to treat the 2 cm increase as the full height of every box. The bottom box contributes its full height, while each additional nested box adds only 2 cm.
How to fix it at home →Wrong answers children often give:
- 20 Calculation slip
- 25 Calculation slip
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