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Whole numbersStructured · 3 marks

Four boxes each hold a 3-digit number of stickers. The average number of stickers in the four boxes is 250. Two of the boxes hold 185 and 240 stickers. Each of the other two boxes holds a 3-digit number of stickers.

  1. Find the total number of stickers in the other two boxes.
  2. What is the largest possible difference between the number of stickers in these two boxes?
Need a hint?

Start with the total from the average, then take away the two known boxes. For the biggest gap, one number must be as small as possible.

Worked answer

  1. Total of the four boxes: 4 × 250 = 1000.
  2. Stickers in the two known boxes: 185 + 240 = 425.
  3. (a) Other two boxes: 1000 − 425 = 575.
  4. To make the difference largest, make one box as small as possible: 100 stickers.
  5. The other box then has 575 − 100 = 475 stickers.
  6. (b) Largest difference: 475 − 100 = 375.
Answer: 375 stickers

The mistake this question tests

Habit

Average and total

Pupils often stop at 475, the larger of the two numbers, and forget to subtract the smaller number 100.

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