Bob's 9th-grade class is renting out a bowling alley for a party. The bowling alley charges a flat rate of $300, plus an additional $4 per student. So far, 25 students have signed up to attend the party, and more students will probably sign up before the deadline next week.Find an expression for f(x), the total number of students who will come to the party if x students sign up between now and the deadline.f(x)=Next, find an expression for g(x), the total cost of the party if x students sign up between now and the deadline.g(x)=If the students split the total cost so that each student at the party pays the same amount, which function tells you how much each student will pay?
Question
Bob's 9th-grade class is renting out a bowling alley for a party. The bowling alley charges a flat rate of 4 per student. So far, 25 students have signed up to attend the party, and more students will probably sign up before the deadline next week.Find an expression for f(x), the total number of students who will come to the party if x students sign up between now and the deadline.f(x)=Next, find an expression for g(x), the total cost of the party if x students sign up between now and the deadline.g(x)=If the students split the total cost so that each student at the party pays the same amount, which function tells you how much each student will pay?
Solution
The expression for f(x), the total number of students who will come to the party if x students sign up between now and the deadline, is:
f(x) = 25 + x
This is because 25 students have already signed up, and x is the number of additional students that sign up.
Next, the expression for g(x), the total cost of the party if x students sign up between now and the deadline, is:
g(x) = 300 + 4*(25 + x)
This is because the bowling alley charges a flat rate of 4 per student. The total number of students is 25 + x.
If the students split the total cost so that each student at the party pays the same amount, the function that tells you how much each student will pay is:
h(x) = g(x) / f(x)
This is because the total cost g(x) is divided equally among the total number of students f(x).
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