Peggy sue decided to enter her famous five alarm chili at her local chili cooking contest normally she needs five tomatoes to make enough chili for her family of seven how many tomatoes what should she expect to use to make her famous recipe for 100 people

If the normal chili means

5 tomatoes = 7
then 
x tomatoes = 100 
dividing both equations and solving for x we have

5/x = 7/100
x = (100/7)*5
x = 71.43 tomatoes 
x ≈ 72 tomatoes

This is a problem of direct relation or proportion.

The number of tomatoes to make the chili is proportional to the number of people in this way

5 tomatoes / 7 people = x tomatoes / 100 people

Solve for x: x = 5 tomatoes * 100 people / 7 people = 71. 42 tomates.

About 71 tomatoes and a piece (less than half) of other.

I think 71 tomatoes is enough, but she could use 72 if she wants to be 100% sure, given that her chilli is so good.