Problem 21 · 2010 Math Kangaroo
Stretch
Algebra & Patterns
arithmetic-sequenceoff-by-one
In front of a supermarket there are two rows of interconnected trolleys. The first one is 2.9 m long and consists of 10 trolleys. The second one is 4.9 m long and consists of twenty trolleys. How long is one trolley?
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Answer: C — 1.1 m
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Hint 1 of 2
Each extra trolley adds the same small length to a row.
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Hint 2 of 2
Use the two rows to find that per-extra-trolley length, then back out one trolley.
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Approach: constant increment per added trolley
- 10 trolleys: L + 9d = 2.9; 20 trolleys: L + 19d = 4.9.
- Subtracting, 10d = 2.0, so each extra trolley adds d = 0.2 m.
- Then L = 2.9 - 9(0.2) = 1.1 m for one trolley.
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