Question 1142738
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Let x be the number of suits that the first company produces per day.


Then the number of suits that the second company produces per day is (x+4), according to the condition.


The first company completed its order in  {{{810/x}}}  days.


The second company completed its order in  {{{900/(x+4)}}} days.


The difference is 6-3 = 3 days.


    {{{810/x}}} - {{{900/(x+4)}}} = 3   days.



The setup is completed.


To solve the equation, multiply both sides by x*(x+4)


    810*(x+4) - 900x = 3x*(x+4)

    810x + 3240 - 900x = 3x^2 + 12x

    3x^2 + 102x - 3240 = 0

    x^2  + 34x - 1080 = 0

    {{{x[1,2]}}} = {{{(-34 +- sqrt(34^2 + 4*1080))/2}}} = {{{(-34 +- 74)/2}}}.


Only positive root  x = {{{(-34 + 74)/2}}} = 20 makes sense.


<U>ANSWER</U>.  20 suits per day for the first company and 20+4 = 24 suits per day for the second company.


<U>CHECK</U>.   {{{810/20}}} - {{{900/24}}} = 40.5 - 37.5 = 3 days.   ! Correct !
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Solved.