William and Debra Pierce are celebrating their 20th anniversary by having a reception at a local reception hall. They have budgeted $3,000 for their reception. If the reception hall charges a $80 cleanup fee plus $32 per person, find the greatest number of people that they may invite and still stay within their budget.
William and Debra can invite at most __ people to the reception. (Round down to the nearest whole person.)
First, we need to subtract the $80 cleanup fee from the total budget of $3,000: $3,000 - $80 = $<<3000-80=2920>>2,920
Next, we need to divide the remaining budget by the cost per person to find the maximum number of people they can invite: $2,920 / $32/person = <<2920/32=91.25>>91.25 people
Since they cannot invite a fraction of a person, they can invite at most 91 people to the reception.
To find the greatest number of people William and Debra can invite, we need to determine the maximum number of guests that will still keep them within their budget.
Let:
- x be the number of guests they can invite.
- $80 be the cleanup fee.
- $32 be the cost per person.
The total cost of the reception will be $80 (cleanup fee) plus $32 (cost per person) multiplied by the number of guests (x):
Total Cost = $80 + $32x
We know that the total cost should not exceed their budget of $3,000. Thus, we can set up the following inequality:
$80 + $32x ≤ $3,000
To solve for x, we will subtract $80 from both sides of the inequality:
$32x ≤ $3,000 - $80
$32x ≤ $2,920
Dividing both sides of the inequality by $32, we can find the maximum number of guests:
x ≤ $2,920 ÷ $32
x ≤ 91.25
Since we need to round down to the nearest whole person, William and Debra can invite at most 91 people to their reception.
To find the greatest number of people that William and Debra can invite to the reception while staying within their budget, we need to set up an equation using the given information.
Let's assume the number of people they can invite is "x".
According to the information given, the reception hall charges a $80 cleanup fee plus $32 per person. Therefore, the total cost of the reception can be represented by:
Total cost = $80 (cleanup fee) + $32/person (number of people)
We want the total cost to be within their budget of $3,000, so we can set up the equation as follows:
Total cost ≤ Budget
$80 + $32x ≤ $3,000
Now, we can solve this equation to find the maximum value of "x" that satisfies the inequality.
$32x ≤ $3,000 - $80
$32x ≤ $2,920
x ≤ $2,920 / $32
x ≤ 91.25
Since we need to round down to the nearest whole person, William and Debra can invite at most 91 people to the reception.