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?
Accepted Solution
A:
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.