Answer:
The system of equation to find the length of service call is
.
The length of service call for which both businesses charge the same amount is 5 hours.
Step-by-step explanation:
Given:
Let the 'x' represents number of hours of labor.
Also Let the 'y' represent the Total charge.
For Business A:
Fixed charge = $50
Charge of labor for each hour = $36
Amount of total charge is the sum of fixed charge and charge of labor for each hour multiplied number of hours of labor
framing in equation form, we get;
![y=50 +36x \ \ \ \ equation \ 1](https://tex.z-dn.net/?f=y%3D50%20%2B36x%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%201)
For Business B:
Fixed charge = $35
Charge of labor for each hour = $39
Amount of total charge is the sum of fixed charge and charge of labor for each hour multiplied number of hours of labor
framing in equation form, we get;
![y =35 +39x \ \ \ \ equation \ 2](https://tex.z-dn.net/?f=y%20%3D35%20%2B39x%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%202)
Hence The system of equation to find the length of service call is
.
Now to find the length of service call for which both businesses charge the same amount, we will make both the equation equal we get;
![50+36x=35+39x](https://tex.z-dn.net/?f=50%2B36x%3D35%2B39x)
Now we solve the equation,
Combining the like terms, we get;
![50-35=39x-36x\\\\15=3x](https://tex.z-dn.net/?f=50-35%3D39x-36x%5C%5C%5C%5C15%3D3x)
Dividing both side by '3' using division property, we get;
![\frac{15}{3}=\frac{3x}{3}\\\\5=x](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B3%7D%3D%5Cfrac%7B3x%7D%7B3%7D%5C%5C%5C%5C5%3Dx)
Hence The length of service call for which both businesses charge the same amount is 5 hours.