Question

A school group wants to rent part of a bowling alley to have a party. The bowling alley costs $500 to rent, plus an additional charge of $5 per student to bowl. The group doesn’t want any student to pay more than $15 total to attend this party.

What is inequality that could represent this situation?
How many students would need to attend so each student would pay at most $15?

Answer 1

If there are N students, the total cost will be:

C(N) = $500 + $5*N.

And we want the amount that each student pays to be equal or less than $15.

then:

C(N)/N ≤ $15.

Then the inequality that represents this situation is:

($500 + $5*N)/N ≤ $15.

Now, let's solve this:

($500 + $5*N) ≤ $15*N

$500 ≤ $15*N - $5*N

$500 ≤ $10*N

$500/$10 ≤ N

50 ≤ N

So the minimum number of students needed is 50.