Respuesta :
Answer:
The system of equation to find the length of service call is [tex]\left \{ {{y=50 +36x} \atop {y =35 +39x}} \right.[/tex].
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;
[tex]y=50 +36x \ \ \ \ equation \ 1[/tex]
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;
[tex]y =35 +39x \ \ \ \ equation \ 2[/tex]
Hence The system of equation to find the length of service call is [tex]\left \{ {{y=50 +36x} \atop {y =35 +39x}} \right.[/tex].
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;
[tex]50+36x=35+39x[/tex]
Now we solve the equation,
Combining the like terms, we get;
[tex]50-35=39x-36x\\\\15=3x[/tex]
Dividing both side by '3' using division property, we get;
[tex]\frac{15}{3}=\frac{3x}{3}\\\\5=x[/tex]
Hence The length of service call for which both businesses charge the same amount is 5 hours.
