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Steve and Michelle Neely are celebrating their 30th anniversary by having a reception at a local reception hall. They have budgeted $2000 for their reception. If the reception hall charges a $60 cleanup fee plus $30 per person, find the greater number of people that they may invite and still stay within their budget. ( round down to the nearest whole person )

Steve and Michelle Neely are celebrating their 30th anniversary by having a reception at a local reception hall They have budgeted 2000 for their reception If t class=

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We have a budget of $2000. This is the maximum cost of the reception.

The cost has a fixed part, that is $60, and a varaible part, which is $30 per person.

Then, if n is the number of people invited, then the cost can be expressed as:

[tex]C(n)=60+30\cdot n[/tex]

We know that this cost has to be $2000 at most, so we can find n as:

[tex]\begin{gathered} C(n)=60+30n\le2000 \\ 60+30n\le2000 \\ 30n\le2000-60 \\ 30n\le1940 \\ n\le\frac{1940}{30} \\ n\le64.67 \end{gathered}[/tex]

Then, as n ≤ 64.67, the maximum number of people they can invite with this budget is 64 people.

Answer: 64 people.