Problem 18 · 2019 Math Kangaroo
Stretch
Algebra & Patterns
balance-scalesubstitution
4 equally heavy black pearls, 1 white pearl and a piece of iron weighing 30 g are placed on a beam balance, as shown in the diagram, and the balance is level. How heavy are 6 black pearls and 3 white pearls altogether?
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Answer: E — 90 g
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Hint 1 of 3
A level balance means the two sides weigh exactly the same; read off what equals what.
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Hint 2 of 3
From the picture, the pearls left over on one side just balance the 30 g of iron.
Still stuck? Show hint 3 →
Hint 3 of 3
Notice that 6 black and 3 white is simply three copies of that balanced group of pearls.
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Approach: scale the balance equation
- Reading the balanced scale, 2 black pearls and 1 white pearl together weigh the same as the 30 g iron, so 2 black + 1 white = 30 g.
- We want 6 black + 3 white, which is exactly three copies of that group: 3 × (2 black + 1 white).
- So 6 black and 3 white pearls weigh 3 × 30 g = 90 g (E).
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