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

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