Problem 15 · 2024 Math Kangaroo
Hard
Algebra & Patterns
substitution
All trolleys in a shop are the same. Four trolleys slid together have a total length of 108 cm (see diagram). Ten trolleys slid together have a total length of 168 cm. How long is one trolley?
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Answer: C — 78 cm
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Hint 1 of 2
Each extra trolley adds only the part that sticks out past the one in front, a fixed overlap length.
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Hint 2 of 2
Compare 4 trolleys with 10 trolleys to find that fixed added length, then back out one whole trolley.
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Approach: use the difference to find the added length per trolley
- Going from 4 to 10 trolleys adds 6 trolleys and 168 − 108 = 60 cm.
- So each extra trolley adds 60 ÷ 6 = 10 cm.
- Four trolleys = one full trolley + 3 added bits: 108 = L + 3·10, so L = 108 − 30 = 78 cm.
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