Problem 14 · 2010 Math Kangaroo
Medium
Arithmetic & Operations
guess-and-check
A ferry boat can carry, in one trip, either 10 cars or 6 lorries. Yesterday the boat crossed the river 5 times. It was always full and carried 42 vehicles in all. How many of these were cars?
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Answer: E — 30
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Hint 1 of 2
Each of the 5 full trips carries either 10 cars or 6 lorries.
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Hint 2 of 2
Start by pretending every trip was lorries, then see how far short of 42 you are.
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Approach: start from all-lorry trips and swap until the total is right
- If all 5 trips were lorry trips, that would be 6 + 6 + 6 + 6 + 6 = 30 vehicles, which is 12 short of 42.
- Changing one lorry trip (6) into a car trip (10) adds 4 vehicles, and 12 needs three such changes.
- So 3 trips were car trips: 10 + 10 + 10 = 30 cars, choice E.
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