steve and michelle neely are celebrating their 30th anniversary by having a reception at a local reception hall. They have budgeted $4,500 for their reception. If the reception hall charges a $80 cleanup fee plus $30 per​ person, find the greatest number of people that they may invite and still stay within their budget.

Answer 1

Let's denote the number of people they can invite as "x".
The total cost of the reception hall is given by the equation:
80 + 30x = 4500.

To find the greatest number of people they can invite and still stay within their budget, we need to solve for x in the equation above.

Subtracting 80 from both sides of the equation:

30x = 4500 - 80,
30x = 4420.

Dividing both sides by 30:

x = 4420/30,
x ≈ 147.33.

Since it is not possible to invite a fraction of a person, the greatest whole number of people they can invite is 147.

Therefore, they can invite a maximum of 147 guests and still stay within their budget.