Question

a plumber charged $70 for the first 30 minutes of each house call plus $4 for each additional minute he works. if he charges hayden $122 for the house visit how long did the plumber work

Answer 1

The plumber worked for 43 minutes.

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)