To determine the total cost of a ticket, we need to combine the two given functions for the base ticket price and the service charge. The base ticket price is modeled by the function [tex]\( p(x) = 15x + 10 \)[/tex] and the service charge is modeled by the function [tex]\( c(x) = 5x + 2 \)[/tex].
To find the total cost of a ticket, we must perform the addition of these polynomials since we want to add the base price and the service charge together.
Step-by-step, the solution is as follows:
1. Write down the base ticket price function:
[tex]\[ p(x) = 15x + 10 \][/tex]
2. Write down the service charge function:
[tex]\[ c(x) = 5x + 2 \][/tex]
3. To find the total cost of a ticket, add the two functions together:
[tex]\[ T(x) = p(x) + c(x) \][/tex]
4. Substitute the functions into the equation:
[tex]\[ T(x) = (15x + 10) + (5x + 2) \][/tex]
5. Combine the like terms:
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 15x + 5x = 20x \][/tex]
- Combine the constant terms:
[tex]\[ 10 + 2 = 12 \][/tex]
6. The resulting function for the total cost is:
[tex]\[ T(x) = 20x + 12 \][/tex]
Thus, the operation used on the polynomials is addition.
