William and Debra Pierce are celebrating their 20th anniversary by having a reception at a local reception hall. They have budgeted $2,000 for their reception. If the reception hall charges a $50 cleanup fee plus $38 per person, find the greatest number of people that they may invite and still stay within their budget.
Let's call the number of people William and Debra can invite "x".
The cleanup fee is a fixed cost of $50.
The cost per person is $38.
Therefore, the total cost of the reception can be calculated as $38x + $50.
Since the total cost must be within their budget of $2,000, we can set up the following equation:
$38x + $50 ≤ $2,000.
To find the greatest number of people they can invite while staying within their budget, we need to solve the inequality for the maximum value of x.
$38x + $50 ≤ $2,000
$38x ≤ $2,000 - $50
$38x ≤ $1,950
Divide both sides of the inequality by $38 to solve for x:
x ≤ $1,950 / $38
x ≤ 51.32
Since the number of people must be a whole number, the greatest number of people they can invite is 51.
Therefore, William and Debra can invite a maximum of 51 people and still stay within their budget.