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.

Answer 1

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.