Steve and Michelle Neely are celebrating their 30th anniversary by having a reception at a local reception hall. They have budgeted $5,000 for their reception. If the reception hall charges a $80 cleanup fee plus $37 per person, find the greatest number of people that they may invite and still stay within their budget
Steve and Michelle can invite at most people to the reception (Round down to the nearest whole person.)
Let the number of people they can invite be x.
The cost of the reception hall is $80 for cleanup + $37 per person, so the total cost is 80 + 37x.
They have budgeted $5,000, so 80 + 37x ≤ 5000.
Subtracting 80 from both sides and dividing both sides by 37 gives 37x ≤ 4920.
Dividing both sides by 37 gives x ≤ 132.97297297297297.
Rounding down to the nearest whole number gives x ≤ 132.
Therefore, the greatest number of people they may invite and still stay within their budget is 132. Answer: \boxed{132}.