Question

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

Answer 1

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.

Answer 2

Explanation:

The $50 cleanup fee is a "fixed cost."

The "$30 per-person fee is a "variable cost." That is, it varies with the number of people.

"within" means "less than or equal to"

Cost = $50 + $30x [where x = number of people]

Cost ≤ $4500 ["stay within their budget"]

$50 + $30x ≤ $4500 [substitute for cost]

$30x ≤ $4450 [subtract $50 from both sides retains sense of inequality]

x ≤ 148.3333 [divide by +$30 retains sense of inequality]

Mark and Heather may invite up to 148 guests.

[note: to be "≤," always truncate, never round up]

Check:

148 people for $30 each + $50 is $4440+$50 = $4490.

One more person makes it $4520 -- that is too much.

There we go, my bad