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two mechanics worked on a car. the first mechanic worked for 5 hours and the second mechanic worked for 15 hours together they charged a total of $1,225 what was the rate charge per hour by each mechanic if the sum of the two rates was $125 per hour

Respuesta :

Given : two mechanics worked on a car

The first : worked for 5 hours

The second : worked for 15 hours

Total charge for both = $1,225

Let the charge rate per hour for the first is x and for the second is y

So,

[tex]5x+15y=1225[/tex]

the sum of the two rates was $125 per hour​ so,

[tex]x+y=125[/tex]

so, we have the following system of equations :

[tex]\begin{gathered} 5x+15y=1225 \\ x+y=125 \end{gathered}[/tex]

Form the second equation : y = 125 - x

Substitute at the first equation with y to find the value of x

so,

[tex]\begin{gathered} 5x+15\cdot(125-x)=1225 \\ 5x+1875-15x=1225 \\ 5x-15x=1225-1875 \\ -10x=-650 \\ \\ x=\frac{-650}{-10}=65 \\ \\ y=125-x=125-65=60 \end{gathered}[/tex]

so, the rate of the first one who worked 5 hours = $65 per hour

And the rate of the second will be = $60 per hour

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