Patterns & Reasoning

Depth · one concept from first principles · step 2 of 4

To divide exactly, drop the leftover or top it up

There are 84.06 kg84.06\ \text{kg} of walnuts to be packed into sacks holding 2.63 kg2.63\ \text{kg} each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?

Number system
Your answer
How to solve
Strategy Guess and Check — Since walnuts can only be added, the target is the next multiple of the sack size above what is there. Find the highest multiple that fits, step up one, and the gap is the answer.
1STEP 1

Find how many sacks fill up

Count how many whole sacks the walnuts already fill without going over.

2.63 × 31 = 81.53
2STEP 2

Step up to the next full sack

The leftover walnuts would be a part-filled thirty-second sack, so aim to fill it.

2.63 × 32 = 84.16
3STEP 3

Find the shortfall

Subtract what is there from what is needed.

84.16 - 84.06 = 0.1
Answer
0.1 kg
Check the target: 84.06 + 0.1 = 84.16, and 84.16 ÷ 2.63 = 32 exactly.
Takeaway

When you can only add, aim for the next multiple up -- not the nearest one.

  • Find how many sacks fill up
  • Step up to the next full sack
  • Find the shortfall
Where next?
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▶ Practice — 12 problems

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