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Two mechanics worked on a car. The first mechanic charged $65 per hour, and the second mechanic charged $90 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $1750. How long did each mechanic work?

Respuesta :

semsee45

Answer:

First mechanic worked 20 hours and second mechanic worked 5 hours

Step-by-step explanation:

Let the number of hours the first mechanic worked = [tex]a[/tex]

Let the number of hours the second mechanic worked = [tex]b[/tex]

Therefore, we can write 2 equations and then solve them simultaneously:

[tex]a+b=25[/tex]

[tex]65a+90b=1750[/tex]

Rearranging the first equation: [tex]a=25-b[/tex]

and substituting into the second equation to find [tex]b[/tex]:

[tex]65(25-b)+90b=1750[/tex]

[tex]1625-65b+90b=1750\\ 25b=125\\ b=5[/tex]

Now sub [tex]b=5[/tex] into the first equation to find [tex]a[/tex]

[tex]a+5=25\\ a=20[/tex]

Therefore, first mechanic (a) worked 20 hours and second mechanic (b) worked 5 hours

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