Respuesta :
We know that two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $85 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1850.
To find the answer we must represent the situation with a system of equations.
[tex]\begin{gathered} A+B=20\ldots(1) \\ 115A+85B=1850\ldots(2) \end{gathered}[/tex]Where,
A: Number of hours that the first mechanic worked
B: Number of hours that the second mechanic worked
First, we must multiply equation 1 by -115
[tex]\begin{gathered} -115(A+B)=-115\cdot20 \\ -115A-115B=-2300\ldots(3) \end{gathered}[/tex]Second, we must add equations 2 and 3
[tex]\begin{gathered} 115A+85B=1850 \\ -115A-115B=-2300 \\ ---------------- \\ 0-30B=-450\ldots(4) \end{gathered}[/tex]Now, we can solve equation 4 for B
[tex]\begin{gathered} -30B=-450 \\ B=\frac{-450}{-30} \\ B=15 \end{gathered}[/tex]Then, we must replace the value of B in the equation 1 and finally we must solve for A
[tex]\begin{gathered} A+15=20 \\ A=20-15 \\ A=5 \end{gathered}[/tex]Answer:
First mechanic: 5 hours
Second mechanic: 15 hours
