Problem 5 · 2024 Math Kangaroo
Easy
Arithmetic & Operations
work-backward
Pieter has a parcel that weighs 445 g and the eight weights shown. He places the parcel on the right pan of the scale (see picture). Pieter may put weights on either side of the scale. What is the smallest number of weights he needs to balance the scale?
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Answer: B — 3
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Hint 1 of 2
Weights on the parcel's side help it; weights on the other side fight it, so a weight you put with the parcel counts as minus and a weight opposite counts as plus.
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Hint 2 of 2
You need the opposite-side weights minus the parcel-side weights to equal 445 g using as few weights as possible.
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Approach: make 445 as a difference of a few weights
- Putting a weight opposite the parcel adds its value; putting it with the parcel subtracts it, so balancing needs a signed combination equal to 445 g.
- Use 500 on the empty side and 50 + 5 on the parcel's side: 500 − 50 − 5 = 445.
- That is just three weights, and no two-weight combination reaches 445.
- So the minimum number of weights is 3.
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