15 cars containing a total of 60 people crossed a toll bridge. each of the 15 cars contained at least one person but no more than 5 people. at most how many cars contained exactly three people?

If all 15 cars had only 3 people each, the total number of people would be only 45, not 60.

Start with 15 cars with exactly 3 people, and 0 cars with exactly 5 people.

Keep guessing one less car with 3 people and one more car with 5 until the number of people adds to 60 or close to 60.

Cars with 3 people Cars with 5 people

& no. of people & no. of people Total People

15, 45 0, 0 45

14, 42 1, 5 47

13, 39 2, 10 49

12, 36 3, 15 51

11, 33 4, 20 53

10, 30 5, 25 55

9, 27 6, 30 57

8, 24 7, 35 59

7, 21 8, 40 61

It looks like the there are at most 7 cars with exactly 3 people.

Now we need to adjust the 8 other cars, so the total is 60 people.

7 cars with exactly 3 people.

7 cars with exactly 5 people.

1 car with exactly 4 people.

Total People: 60

Answer: At most there can be 7 cars with exactly 3 people.