Q11. - Algebra 1

Question

An electrician charges a \(25 consultation fee plus \)35 per hour for labour.

a. Copy and complete the following table showing the charges for jobs that take 1, 2, 3, 4, or 5 hours.

Hours, $h$	Total cost, $C$
1
2
3
4
5

b. Write an equation in slope-intercept form for the total cost of a job that takes $h$ hours.

c. If the electrician bills in quarter hours, how much would it cost for a job that takes 3 hours 15 minutes to complete?

Step-by-Step Solution

Answer

a. The complete table is:

Hours, $h$	Total cost, $C$
1	60
2	95
3	130
4	165
5	200

b. The equation in slope-intercept form for the total cost of a job that takes $h$ hours is $C=35h+25$, where $C$ represents the total cost of a job and $h$ represents the number of hours.

c. The cost for a job that takes 3 hours 15 minutes to complete is $\mathrm{\$}138.75$.

Part a. Step 1. Find the values of C for the given values of h .

It is given that cost of Labour is $35/hour and consultation fee is $25.

It is given that number of hours is $h$.

As, the cost of labour is $35 for 1 hour. Therefore, the cost of labour for $h$ hours is $35h$.

Let $C$ represents the total cost of job.

Therefore, the total cost of job $C$ is given by:

$$\begin{gathered} C=\text{cost of labour for }h\text{ hour}+\text{consultation fee} \\ =35h+25 \end{gathered}$$

 

Find the values of $C$ for the given values of $h$.

When $h=1$,

$$\begin{gathered} C=35\left(1\right)+25 \\ =35+25 \\ =60 \end{gathered}$$

When $h=2$,

$$\begin{gathered} C=35\left(2\right)+25 \\ =70+25 \\ =95 \end{gathered}$$

When $h=3$,

$$\begin{gathered} C=35\left(3\right)+25 \\ =105+25 \\ =130 \end{gathered}$$

When $h=4$,

$$\begin{gathered} C=35\left(4\right)+25 \\ =140+25 \\ =165 \end{gathered}$$

When $h=5$,

$$\begin{gathered} C=35\left(5\right)+25 \\ =175+25 \\ =200 \end{gathered}$$

Part a. Step 2. Write the complete table.

The complete table is:

Hours, $h$	Total cost, $C$
1	60
2	95
3	130
4	165
5	200

Part b. Step 1. Write the slope-intercept form of a line.

The equation of line in slope-intercept form is:

$y=mx+b$

Where $m$ is the slope of the line and $b$ is the $y$-intercept of the line.

Part b. Step 2. Write the equation in slope-intercept form for the total cost of a job that takes h hours.

The equation in slope-intercept form for the total cost of a job that takes $h$ hours is $C=35h+25$ where $C$ represents the total cost of a job and $h$ represents the number of hours.

Part c. Step 1. Write the equation for the total cost of a job.

The equation in slope-intercept form for the total cost of a job that takes $h$ hours is $C=35h+25$ where $C$ represents the total cost of a job and $h$ represents the number of hours.

Part c. Step 2. Determine the cost for a job that takes 3 hours 15 minutes to complete.

The time 3 hours 15 minutes in hours is given by:

$$\begin{gathered} 3\text{ hours }15\text{ minutes}=3\text{ hours}+15\text{ minutes} \\ =3\text{ hours}+\frac{15}{60}\text{ hours} \\ =3\text{ hours}+\frac{1}{4}\text{ hours }\left(\because \text{ 1 hour}=60\text{ minutes}\right) \\ =\left(3+\frac{1}{4}\right)\text{ hours} \\ =\frac{13}{4}\text{ hours} \end{gathered}$$

The cost for a job that takes $\frac{13}{4}$ hours to complete can be find out be substituting $\frac{13}{4}$ for $h$ in the equation $C=35h+25$.

Therefore, it is obtained that:

$$\begin{gathered} C=35h+25 \\ =35\left(\frac{13}{4}\right)+25 \\ =\frac{35\times 13}{4}+25 \\ =\frac{455+100}{4} \\ =\frac{555}{4} \\ =138.75 \end{gathered}$$

Therefore, the cost for a job that takes 3 hours 15 minutes to complete is $\mathrm{\$}138.75$.