Answer:
Step-by-step 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
Answer:
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.
