Question

You need to hire a catering company to serve meals to guests at a wedding reception. Company A charges $500 plus $20 per guest. Company B charges $800 plus $16 per guest. For how many guests are the total costs the same at both companies?

Set up the Cost equations for both companies where g is the number of guests:
C(a) = 20g + 500
C(b) = 16g + 800

Answer 1

The answer is 75 guests.

Explanation:

Let the number of guests be represented by g.

Company A charges $500 plus $20 per guest. Equation forms:

`500+20g` ......(1)

Company B charges $800 plus $16 per guest. Equation forms:

`800+16g` ......(2)

To know the number of guests to get the total costs of both companies as same, we will equal both equations:

`500+20g=800+16g`

Solving for g;

`20g-16g=800-500`

=>
`4g=300`

=> g = 75

Hence, 75 guests are needed to get costs for both companies same.