Problem 13 · 2023 Math Kangaroo
Hard
Arithmetic & Operations
sum-constraint
In a queue in front of a ferry there are 8 cars with 19 people in total. There are either 2 or 3 people in each car. How many cars are there with exactly 2 people?
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Answer: D — 5
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Hint 1 of 2
If every car held 2 people there would be only 16; you need 3 more.
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Hint 2 of 2
Each car upgraded from 2 to 3 people adds exactly one person.
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Approach: start from all-twos and account for the extra people
- Eight cars with 2 people each would carry 16 people, but there are 19.
- The 3 extra people come from 3 cars holding 3 instead of 2.
- So 8 − 3 = 5 cars hold exactly 2 people.
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