Question

One caterer charges a basic fee of $\$100$ plus $\$15$ per person. A second caterer charges a basic fee of $\$200$ plus $\$12$ per person. What is the least number of people for which the second caterer is cheaper?

Answer 1

Let n be the number of people. Compare costs:

First: 100 + 15n
Second: 200 + 12n

We need 200 + 12n < 100 + 15n, so 100 < 3n, hence n > 100/3 ≈ 33.33. The least integer n satisfying this is 34.

Answer: 34 people.