Respuesta :
Answer:
The mechanic who worked for 15 hours charged $55 per hour, while the mechanic that worked for 5 hours charged $80 per hour.
Given:
x = rate of the mechanic who worked 15 hours
y = rate of the mechanic who worked 5 hours
Since the total of their rates is $135, we cuold express it as
x + y = 135
Then, since they are charges a total of $1225 after working, we could express it as
15x + 5y = 1225
Now that we have two expressions:
x + y = 135.................Equation 1
15x + 5y = 1225........Equation 2
We can solve for one variable through substitution
[tex]x+y=135\rightarrow x=135-y[/tex]*Substitute x to the second equation
[tex]15x+5y=1225[/tex][tex]15(135-y)+5y=1225[/tex]*Solve for y
[tex]2025-15y+5y=1225[/tex][tex]-15y+5y=1225-2025[/tex][tex]-10y=-800[/tex]*Divide both sides by -10
[tex]\frac{-10y}{-10}=\frac{-800}{-10}[/tex][tex]y=80[/tex]Now we got a value for y, let us substitute this to the first equation to get the value of x.
[tex]x+y=135[/tex]*Substitute y = 80
[tex]x+(80)=135[/tex][tex]x+80=135[/tex][tex]x=135-80[/tex][tex]x=55[/tex]Now, we got a value for x which is 55.
Going back to our given, since:
x = rate of the mechanic who worked 15 hours
y = rate of the mechanic who worked 5 hours
The mechanic who worked for 15 hours charged $55 per hour, while the mechanic that worked for 5 hours charged $80 per hour.
