Problem 7 · 2015 Math Kangaroo
Medium
Algebra & Patterns
balance-scalesubstitution
The two birds Rita and Dita are weighed on balance scales (see picture). How much does Dita weigh?
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Answer: D — 5 kg
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Hint 1 of 2
The first balance tells you the two birds together weigh a fixed amount.
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Hint 2 of 2
The second balance compares one bird (with the small weight) against the other, giving the difference between them.
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Approach: use the sum and the difference of the two weights
- The first scale shows the two birds together balance 8 kg, so Rita and Dita's weights add to 8.
- The second scale shows Dita is heavier than Rita by exactly the 2 kg weight, so Dita is 2 kg more than Rita.
- Two numbers that add to 8 and differ by 2 are 3 and 5, so the heavier bird Dita weighs 5 kg.
With a letter
If Rita = r, then Dita = r + 2 and r + (r + 2) = 8, so r = 3 and Dita = 5.
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