steve and michele are celebrating their 30th anniversary by having a reception at a local reception hall. They have budgeted f3,000 for their reception. If the reception hall charges a $100 cleanup fee plus $36 per person, find the greatest number of people that they may invite and still stay within their budget.
Let's denote the number of people they can invite as 'x'.
The cost of the cleanup fee is $100, and the cost per person is $36. Therefore, the total cost is given by the equation:
$100 + $36*x = $3000
Subtracting $100 from both sides of the equation, we get:
$36*x = $2900
Dividing both sides of the equation by $36, we get:
x = $2900 / $36
Simplifying the right side of the equation, we get:
x = 80.56
Since the number of people must be a whole number, the greatest number of people they can invite is 80. Answer: \boxed{80}.
To find the greatest number of people that Steve and Michele can invite and stay within their budget, we'll set up an equation:
Let x be the number of people they invite.
The total cost of the reception will be the cleanup fee plus the cost per person multiplied by the number of people:
Total cost = Cleanup fee + (Cost per person × Number of people)
Since the total cost must stay within their budget of $3,000, we can write the equation:
Cleanup fee + (Cost per person × Number of people) ≤ $3,000
Substituting the given values, the equation becomes:
$100 + ($36 × x) ≤ $3000
To find the greatest number of people they can invite, we need to solve this equation for x.
First, subtract $100 from both sides:
$36x ≤ $3000 - $100
$36x ≤ $2900
Next, divide both sides by $36:
x ≤ $2900 / $36
x ≤ 80.56
Since we can't invite a fraction of a person, we round down to the nearest whole number:
x ≤ 80
Therefore, the greatest number of people Steve and Michele can invite and still stay within their budget is 80.
To determine the greatest number of people Steve and Michele can invite while staying within their budget, we need to find the maximum number of people that will not exceed their budget of $3,000.
Let's break down the cost of the reception:
- There is a $100 cleanup fee that is charged regardless of the number of people.
- There is an additional charge of $36 per person attending the reception.
Let's assume the number of people they can invite is "x". Therefore, the cost of the reception would be:
Cost = Cleanup fee + (Number of people * Cost per person)
From the given information, we can set up an equation:
3000 = 100 + (x * 36)
Now, we can solve this equation to find the value of "x":
3000 - 100 = 36x
2900 = 36x
x = 2900 / 36
x = 80.55
Since you can't invite a fraction of a person, we need to round down to the nearest whole number. Therefore, the greatest number of people Steve and Michele can invite and stay within their budget is 80 people.
Note: Keep in mind that this calculation assumes that all costs other than the cleanup fee and the cost per person are accounted for in the $3,000 budget.