Problem 8 · 2021 Math Kangaroo
Easy
Logic & Word Problems
balance-reasoningwork-backward
Rosana has some balls of 3 different colours. Balls of the same colour have the same weight. What is the weight of each white ball?
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Answer: C — 5
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Hint 1 of 2
Look at the two scales that both have a black ball and a grey ball on them, and compare what is different.
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Hint 2 of 2
Find the grey ball's weight first, then the black ball's, and only then the white ball.
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Approach: compare the scales to find one colour at a time, then the white ball
- One grey and one black ball together weigh 6, while one black and two grey balls together weigh 10.
- The second scale is just the first scale with one extra grey ball, and it is 10 - 6 = 4 heavier, so one grey ball weighs 4 (and the black ball weighs 6 - 4 = 2).
- Two white balls plus one grey ball weigh 14, so the two white balls weigh 14 - 4 = 10, which means each white ball weighs 5.
- So each white ball weighs 5 (C).
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