Question

Mark and Heather starr are celebrating thier 25th anniversary by a reception at a local reception hall. They have budgeted $4,000 for thier reception. If the reception hall charges a $80 cleanup fee plus $36 per person. Find the greatest number of people that they may invite and still stay with in thier budget?

Answer 1

Mark and Heather Starr can invite up to 108 guests to their reception while staying within their budget of $4,000, after accounting for an $80 cleanup fee and $36 per person charge.

Step-by-step explanation:

To find the greatest number of people that Mark and Heather Starr may invite to their reception without exceeding their budget of $4,000, we need to take into account the fixed cleanup fee and the per-person charge. The reception hall charges a $80 cleanup fee plus $36 per person. To calculate the number of guests they can afford to invite, we will subtract the cleanup fee from the total budget and then divide the result by the per-person charge.

The calculation is as follows:

1. Subtract the cleanup fee from the total budget: $4,000 - $80 = $3,920.
2. Divide the remaining budget by the per-person charge: $3,920 / $36 ≈ 108.89.

Since they cannot invite a fraction of a person, the greatest whole number of people they can invite is 108 guests.

Let x be the number of people invited. The equation representing the total cost of the reception is: $80 + $36x = $4,000. We can solve this equation by subtracting $80 from both sides and dividing by $36. This gives us the equation: $36x = $3,920. Dividing both sides by $36, we find that x = 109. Therefore, Mark and Heather can invite a maximum of 109 people and still stay within their budget.