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- anonymous

Two mechanics worked on a car. The first mechanic charged $75 per hour, and the second mechanic charged $110 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $2025. How long did each mechanic work?
Will medal

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- anonymous

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- jdoe0001

so.. let's say hmmm the hours the $75 mechanic worked was \(\bf x\)
and the hours the $110 mechanic worked was \(\bf y\)
how many hours did they work together?

- anonymous

20

- jdoe0001

so... they worked together 20 hours
we dunno what those hours are, but we can call them "x" and "y"
so we could say that
\(\bf x+y=20\)
the mechanic that charges $75 per hour, after "x" hours, he ended up charging 75*x or 75x
the mechanic that charges $110 per hour, after "y" hours, he ended up charging 110*y or 110y
now, their total bill was 2025
so we could also say that
\(\bf 75x+110y = 2025\)
any ideas?

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- anonymous

im confused
i have to give hours for mechanic one and mechanic 2

- anonymous

i have 4 questions like this i really want to know how tp figure them out

- jdoe0001

yes....
notice... x+y = 20
so... if you solve that for say "y"... how does it look like?

- jdoe0001

the hours, notice above, for each is "x" and "y", thus

- texaschic101

this is basically a substitution problem involving the 2 equations up above ^^.
We have :
x + y = 20 ----> x = -y + 20
75x + 110y = 2025
now sub -y + 20 in for x back into the second equation....you will then be solving for y, the hrs for the mechanic that charges 110 per hr.

- anonymous

mechanic 1 5 hours
mechanic 2 15 hours ??

- texaschic101

lets check by subbing in your answers into the 2nd equation..
75x + 110y = 2025
75(5) + 110(15) = 2025
375 + 1650 = 2025
2025 = 2025 (correct)
yes...that is correct

- anonymous

ty for explaining it

- texaschic101

medal should go to jdoe....he/she helped you set it up...without that, you have nothing...lol

- anonymous

you stayed to make sure i understood..

- texaschic101

all is good...I gave jdoe a medal
I am always happy to help when I can :)

- anonymous

ty

- texaschic101

:)

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