a couple are celebrating their 10th anniversary by having a reception at a local reception hall. they have…

a couple are celebrating their 10th anniversary by having a reception at a local reception hall. they have budgeted $3,500 for their reception. if the reception hall charges a $60 cleanup fee plus $35 per person, find the greatest number of people that they may invite and still stay within their budget. the couple can invite at most □ people to the reception. (round down to the nearest whole person.)

a couple are celebrating their 10th anniversary by having a reception at a local reception hall. they have budgeted $3,500 for their reception. if the reception hall charges a $60 cleanup fee plus $35 per person, find the greatest number of people that they may invite and still stay within their budget. the couple can invite at most □ people to the reception. (round down to the nearest whole person.)

Answer

Explanation:

Step1: Set up cost - equation

Let the number of people be $x$. The total cost $C$ is the sum of the cleanup fee and the cost per person. So $C = 60+35x$. The budget is $3500$. We set up the inequality $60 + 35x\leq3500$.

Step2: Solve the inequality for $x$

First, subtract 60 from both sides of the inequality: $35x\leq3500 - 60$, so $35x\leq3440$. Then divide both sides by 35: $x\leq\frac{3440}{35}\approx98.2857$.

Step3: Round down to the nearest whole person

Since $x$ represents the number of people and we need to stay within the budget, we round down $98.2857$ to 98.

Answer:

98