SOLUTION: 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

Producing x items per day, it will take    days to make 400 items.


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


The difference   -   is 10 days, according to the problem.


So we have this "time" equation

     -  = 10   days.      (1)


Dividing both sides by 10 gives

     -  = 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.    ANSWER


CHECK.  We will check the starting equation (1)


         -  =  -  = 20 - 10 = 10  days.    ! Correct !