SOLUTION: A company has an order for 810 suits, another company has to make 900 suits in the same period of time. The first company has completed its task 3 days ahead of time and the second

Algebra ->  Human-and-algebraic-language -> SOLUTION: A company has an order for 810 suits, another company has to make 900 suits in the same period of time. The first company has completed its task 3 days ahead of time and the second      Log On


   

Question 1142738: A company has an order for 810 suits, another company has to make 900 suits in the same period of time. The first company has completed its task 3 days ahead of time and the second company 6 days ahead of time. How many suits does each company produce per day, if the second company makes 4 suits per day more than the first?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.
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%2Fx  days.


The second company completed its order in  900%2F%28x%2B4%29 days.


The difference is 6-3 = 3 days.


    810%2Fx - 900%2F%28x%2B4%29 = 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%5B1%2C2%5D = %28-34+%2B-+sqrt%2834%5E2+%2B+4%2A1080%29%29%2F2 = %28-34+%2B-+74%29%2F2.


Only positive root  x = %28-34+%2B+74%29%2F2 = 20 makes sense.


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


CHECK.   810%2F20 - 900%2F24 = 40.5 - 37.5 = 3 days.   ! Correct !

Solved.


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i get the following.

we have company A and company B.

company A has an order for 810 suits.
company B has an order for 900 suits in the same period of time.

company A completes its task 3 days ahead of time.
company B completes its task 7 days ahead of time.

company B make 4 more suits per day than company A.

the general formula to use is R * T = Q

R is the number of suits produced per day.
T is the number of days.
Q is the number of suits produced.

for company A, the formula becomes R * (T-3) = 810
for company B, the formula becomes (R+4) * (T-6) = 900

solve for R in the first equation to get R = 810/(T-3)

replace R in the second equation by 810/(T-3) to get:
(810/(T-3))+4) * (T-6) = 900
multiply both sides of this equation by (T-3) to get:
(810 + 4 * (T-3)) * (T-6) = 900 * (T-3)
simplify to get:
(810 + 4*T - 12) * (T - 6) = 900*T - 2700
simplify further to get:
(798 + 4*T) * (T - 6) = 900*T - 2700
simplify further to get:
798*T - 4788 + 4*T^2 - 24*T = 900*T - 2700
subtract 900*T from both sides of the equation and add 2700 to both sides of the equation and order the terms in descending order of degree to get:
4*T^2 - 126*% - 2088 = 0
factor this quadratic equation to get:
T = 43.5 or T = -12

T has to be positive so T = 43.5
since R = 810 / (T-3), you get:
R = 20

your solution appears to be that company A produces 20 suits per day and company B produces 24 suits per day.

company A finishes 3 days ahead of time, so company A finishes in 40.5 days.
company B finishes 6 days ahead of time, so company B finishes in 37.5 days.

20 * 40.5 = 810
24 * 37.5 = 900

the numbers check out so it appears the solution is good.

the solution is that company A produces 20 suits per day and company B produces 24 suits per day.