Answer:
The plumber worked for 43 minutes.
Step-by-step explanation:
A plumber charged $70 for the first 30 minutes of each house call plus $4 for each additional minute he works.
Now, the total amount to be paid to the plumber C(x) as a function of x number of minutes that he works can be modeled by the equation
C(x) = 70 for x ≤ 30 minutes and C(x) = 70 + (x - 30)4 for x > 30 minutes.
Now, the plumber charges Hayden $122 for the house visit. In that case, x must be greater than 30 minutes.
So, we can write
122 = 70 + (x - 30)4
⇒ 122 = 70 + 4x - 120
⇒ 4x = 172
⇒ x = 43 minutes.
Therefore, the plumber worked for 43 minutes. (Answer)
