Problem 24 · 2021 Math Kangaroo
Stretch
Logic & Word Problems
balance-reasoningsubstitution
Martin placed 3 different types of objects — hexagons, squares and triangles — on sets of scales, as shown. What does he need to put on the left-hand side of the third set of scales for these scales to balance?
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Answer: A — 1 square
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Hint 1 of 2
Each balanced scale tells you that the two sides weigh the same; measure everything in squares.
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Hint 2 of 2
Find how many squares a triangle is worth, then a hexagon, and compare the two sides of the third scale.
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Approach: measure every object in squares, then balance the third scale
- Scale 2: a triangle and a hexagon balance a hexagon and 5 squares, so the triangle weighs 5 squares.
- Scale 1: 2 hexagons balance a triangle and a square, that is 5 + 1 = 6 squares, so 1 hexagon = 3 squares.
- Scale 3 left side is 3 hexagons = 9 squares; the right side is 2 triangles = 10 squares, so the left is 1 square too light.
- He needs to add 1 square (A).
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