Question 1131150
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Let x = the carpenter's hourly rate (in dollars), and h = time in hours the carpenter worked.


Then the apprentice's hourly rate is (x-6) dollars, and his (or her (?)) working time is (h+10) hours.


Then from the condition, you have this system of equations


    x*h = 720,              (1)
    (x-6)*(h+10) = 720      (2)


To solve the system, first FOIL equation (2). You will get


    xh - 6h + 10x - 60 = 720.    (3)


In (3), replace xh by 720, based on (1).  You will get


    720 - 6h + 10x - 60 = 720,   which is simplified to


    10x - 6h = 60.               (4)


Write equation (1) as  

    6xh = 6*720;                 (5)


from equation (4), express 6h = 10x - 60  and substitute it into equation (5).  You will get

    (10x - 60)*x = 6*720,

    10x^2 - 60x + 6*720 = 0,

    x^2 - 6x + 6*72 = 0,

    (x-24)*(x+18) = 0.


Of two solutions  x= 24  and  x= -18,  only positive solution  x= 24  is meaningful, giving the


<U>ANSWER</U>.  The carpenter's hourly rate is  $24 per hour.


<U>CHECK</U>.   The carpenter's working time is  h= 720/24 = 30 hours.


         The apprentice's hourly rate is  $24 - $6 = $18 and his (or her (?) ) working time is  30+10 = 40 hours.


         Both products  24*30  and  18*40  are equal to 720  dollars.   ! Correct !
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Solved.