Question 1110784
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<pre>
55*x + 80*(25-x) = 1750

55x + 2000 - 80x = 1750

-25x = 1750-2000

-25x = -250   ====>  x = {{{(-250)/(-25)}}} = 10.


<U>Answer</U>.  1-st mechanic worked 10 hours.

         2-nd mechanic worked 25-10 = 15 hours.


<U>Check</U>.  10*55 + 15*80 = 1750.    ! Correct !
</pre>

Solved.


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<U>Be aware</U>:  The solution by @josgarithmetic and his answer  &nbsp;&nbsp;20 hours  &nbsp;&nbsp;and &nbsp;&nbsp;25 hours  &nbsp;&nbsp;are &nbsp;&nbsp;<U>W R O N G</U>.



<H3>&nbsp;&nbsp;&nbsp;&nbsp;josgarithmetic, don't you think that it is JUST TIME for you to leave this forum FOREVER ? ? ?</H3>