Answer:
[tex]2d^2-d+5[/tex]
Step-by-step explanation:
The total number of burgers sold from a restaurant from Monday to Sunday:
[tex]f(d)=200d^3+542d^2+179d+1605[/tex]
The number of visitors to the restaurant from Monday to Sunday:
[tex]g(d)=100d+321[/tex]
To find the average number of burgers per person, just divide [tex]f(d)[/tex] by [tex]g(d).[/tex]
First, multiply [tex]g(d)[/tex] by [tex]2d^2[/tex] and subtract the result from [tex]f(d)[/tex]:
[tex]200d^3+542d^2+179d+1605-2d^2(100d+321)\\ \\=200d^3+542d^2+179d+1605-200d^3-642d^2\\ \\=-100d^2+179d+1605[/tex]
Then, multiply [tex]g(d)[/tex] by [tex]-d[/tex] and subtract the result from [tex]-100d^2+179d+1605[/tex]:
[tex]-100d^2+179d+1605-(-d)(100d+321)\\ \\=-100d^2+179d+1605+100d^2+321d\\ \\=500d+1605[/tex]
Now, multiply [tex]g(d)[/tex] by [tex]5[/tex] and subtract the result from [tex]500d+1605[/tex]:
[tex]500d+1605-5(100d+321)\\ \\=500d+1605-500d-1605\\ \\=0[/tex]
Hence,
[tex]f(d)=g(d)(2d^2-d+5)[/tex]
and the function
[tex]b(d)=2d^2-d+5[/tex]
represents the average number of burgers per person.
