Question

The price of a 2-hour plumbing repair job is $150and the price of a 5-hour job is $330. Write an equation for the cost C of a t-hour repair job and use the equation to find the cost of a repair job lasting 6 hours

Answer 1

Given:

The price of a 2-hour plumbing repair job is $150

And the price of a 5-hour job is $330.

The general equation will have the form:

`C=m\cdot t+b`

Where t is the hours and C is the cost:

By the given information, we can write the following equations:

`\begin{gathered} 150=2m+b\rightarrow(1) \\ 330=5m+b\rightarrow(2) \end{gathered}`

Solving the equations to find the values of m and b:

Subtract (1) from (2):

`\begin{gathered} 330-150=5m-2m \\ 180=3m \\ m=(180)/(3)=60 \end{gathered}`

Substitute with (m) into equation (1) to find (b):

`\begin{gathered} 150=2\cdot60+b \\ 150=120+b \\ b=150-120=30 \end{gathered}`

So, the equation will be:

`C=60t+30`

When t = 6 hours:

`C=60\cdot6+30=360+30=390`

So, the answer will be option b. C = 60t + 30; 390