mark and heather starr are celebrating their 25th anniversary by having a reception at local reception hall. they have budget 4500 for their reception. if the reception hall charges 50 cleanup fee plus 30 per person find the greatest number of people they may invite

Step-by-step explanation:

First we need a linear equation for the situation. 50 cleanup fee applies regardless of how many people they have.  Even if NOBODY shows up, they will be charged $50, so $50 is our y-intercept. If they are charged $30 per person, and we are looking for the number of people they can invite, x will represent the number of people and y will represent the cost of everything. The linear equation is

y = 30x + 50. If they have 4500 to spend, then

4500 = 30x + 50, and now solve it for x:

4450 = 30x and now divide by 30 to get

148 1/3 = x. Now, you can't invite a third of a person, so it would be safe to invite 148 people and you won't go over your budget.