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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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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 !
Solved.