Question

William and Debra Pierce are celebrating their 20 th anniversary by having a reception at a local reception hall. They have budgeted $3,000 for their reception. If the reception hall charges a $ 100 cleanup fee plus $ 37 per​ person, find the greatest number of people that they may invite and still stay within their budget

Answer 1

The greatest number of people that they may invite is 78.

Explanation

Suppose, the number of people that they may invite is $x$

The reception hall charges $ 37 per​ person, so the cost for $x$ number of people $=37x$ dollar. It also charges a $ 100 cleanup fee.

Given that, the maximum budget for their reception is $3000. So, the equation will be......

$37x+100\leq 3000\\ \\ 37x\leq 2900\\ \\ x\leq \frac{2900}{37}\\ \\ x\leq 78.378...$

As the number of people will be as a whole number, so the greatest number of people that they may invite and still stay within their budget is 78.