Question

The total number of burgers sold from a restaurant from Monday to Sunday can be modeled by the function f(d)=200d3+542d2+179d+1605and the number of visitors to the restaurant from Monday to Sunday can be modeled by g(d)=100d+321, where d is the number of days since Monday. What is the average number of burgers per person?

Answer 1

`2d^2-d+5`

Explanation:

The total number of burgers sold from a restaurant from Monday to Sunday:

`f(d)=200d^3+542d^2+179d+1605`

The number of visitors to the restaurant from Monday to Sunday:

`g(d)=100d+321`

To find the average number of burgers per person, just divide
`f(d)` by
`g(d).`

First, multiply
`g(d)` by
`2d^2` and subtract the result from
`f(d)`:

`200d^3+542d^2+179d+1605-2d^2(100d+321)\\ \\=200d^3+542d^2+179d+1605-200d^3-642d^2\\ \\=-100d^2+179d+1605`

Then, multiply
`g(d)` by
`-d` and subtract the result from
`-100d^2+179d+1605`:

`-100d^2+179d+1605-(-d)(100d+321)\\ \\=-100d^2+179d+1605+100d^2+321d\\ \\=500d+1605`

Now, multiply
`g(d)` by
`5` and subtract the result from
`500d+1605`:

`500d+1605-5(100d+321)\\ \\=500d+1605-500d-1605\\ \\=0`

Hence,

`f(d)=g(d)(2d^2-d+5)`

and the function

`b(d)=2d^2-d+5`

represents the average number of burgers per person.