Problem 12 · 2021 Math Kangaroo
Medium
Algebra & Patterns
Fractions, Decimals & Percents
substitutionwork-backward
A jar one fifth filled with water weighs 560 g. The same jar four fifths filled with water weighs 740 g. What is the weight of the empty jar?
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Answer: E — 500 g
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Hint 1 of 2
The difference between the two weighings is the weight of the extra water only.
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Hint 2 of 2
Find what one fifth of the water weighs, then peel it off to leave the jar.
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Approach: subtract to isolate the water, then back out the jar
- Going from one fifth to four fifths adds three fifths of the water: 740 − 560 = 180 g.
- So one fifth of the water weighs 180 ÷ 3 = 60 g.
- The empty jar = 560 − 60 = 500 g.
- So the answer is E.
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