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Two mechanics worked on a car. The first mechanic charged 65 per hour and the second Mechanic charged 100 per hour. The mechanics worked for a combined total of 25 hours and together they charged a total of $2150. How long did each mechanic work

Respuesta :

To solve this problem we have to write an equation for each condition where the first charge is x and the second charge is y so:

For the total hours will be:

[tex]x+y=25[/tex]

and the total charge will be:

[tex]65x+100y=2150[/tex]

We can solve the first equation for x so:

[tex]x=25-y[/tex]

and we replace that in the secon equation so:

[tex]65(25-y)+100y=2150[/tex]

and we solve for y so:

[tex]\begin{gathered} 1625-65+100y=2150 \\ 35y=2150-1625 \\ y=\frac{525}{35} \\ y=15 \end{gathered}[/tex]

And with this value of y we can find x so:

[tex]\begin{gathered} x=25-15 \\ x=10 \end{gathered}[/tex]