At the local movie theater it costs $10.00 for 2 students to see a movie. It costs $15.00 for 3 students, and it costs $20.00 for 4 students. Let the number of students be the input. What is the function rule that relates the number of students to the cost of tickets?
To find the function rule that relates the number of students to the cost of tickets, we need to look for the pattern in the given information.
From the given information, we can see the following:
- For 2 students, the cost is $10.00.
- For 3 students, the cost is $15.00.
- For 4 students, the cost is $20.00.
We can notice that as the number of students increases by 1, the cost increases by $5.00.
Therefore, we can conclude that the function rule that relates the number of students (x) to the cost of tickets (y) is:
y = 5x + 5
This means that the cost of tickets (y) can be found by multiplying the number of students (x) by 5 and then adding 5 to the result.
To find the function rule that relates the number of students to the cost of tickets, we need to identify the pattern between the number of students and the corresponding cost.
From the given information, we can see that as the number of students increases, the cost of tickets also increases. Additionally, we can observe that the cost of tickets increases by $5.00 for each additional student.
Let's define the number of students as "n" and the cost of tickets as "c". Based on the given information, we can construct the following table:
Number of students (n) | Cost of tickets (c)
-----------------------------------
2 | $10.00
3 | $15.00
4 | $20.00
To determine the relationship between "n" and "c," we can subtract 2 from the number of students to find the number of additional students beyond the initial 2. This will tell us how many times the cost increases by $5.00.
For example, when there are 2 students, the number of additional students is 0. When there are 3 students, there is 1 additional student, and when there are 4 students, there are 2 additional students.
Hence, the number of additional students (m) can be calculated as n - 2.
Now, we can express the cost of tickets as a function of the number of students (c = f(n)), as follows:
c = 10 + 5m,
Substituting m = n - 2, we get:
c = 10 + 5(n - 2),
Simplifying further, we have:
c = 10 + 5n - 10,
c = 5n.
Therefore, the function rule that relates the number of students (n) to the cost of tickets (c) is c = 5n.