math help please

Question

A party facility charges $500 for a banquet room and $20 per person. In addition, there is a 20% surcharge on the entire fee. Why would you expect the total cost of the party to be given by a linear function of the number of people, P? Give the function

Answer 1

P(p)=1.2(500+20p) because all the factors contribute to a linear relationship between the total cost and the number of people p, so the function is a linear one with one independent variable. Adding on 20% is the same as multiplying by the factor 100+20=120%=1.2.