Question 1191077
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Normally a factory produces 400 radios in x days. 
IF the factory were to produce 20 more radios each day, then it would take 10 days less to produce 400 radios. 
find x
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<pre>
Producing x items per day, it will take  {{{400/x}}}  days to make 400 items.


Producing (x+20) items each day, it will take  {{{400/(x+20)}}}  days to make 400 items.


The difference  {{{400/x}}} - {{{400/(x+20)}}}  is 10 days, according to the problem.


So we have this "time" equation

    {{{400/x}}} - {{{400/(x+20)}}} = 10   days.      (1)


Dividing both sides by 10 gives

    {{{40/x}}} - {{{40/(x+20)}}} = 1.


At this point, you may guess the solution MENTALLY:  it is  x = 20.


Alternatively, you may reduce it to the quadratic equation and solve it formally.


For it, multiply both sides by x*(x+20).  You will get


    40*(x+20) + 40*x = x*(x+20)

    40x + 800 - 40x = x^2 + 20x

    x^2 + 20x - 800 = 0


Factor left side

    (x-20)*(x+40) = 0


Of the two roots, 20 and -40, we disregard the negative root  x= -40  and accept the positive root x= 20.    <U>ANSWER</U>


<U>CHECK</U>.  We will check the starting equation (1)


        {{{400/20}}} - {{{400/(20+20)}}} = {{{400/20}}} - {{{400/40}}} = 20 - 10 = 10  days.    ! Correct !
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Solved.