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

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(52786) (Show Source): You can put this solution on YOUR website!
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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 days. The second company completed its order in days. The difference is 6-3 = 3 days. - = 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 = = . Only positive root x = = 20 makes sense. ANSWER. 20 suits per day for the first company and 20+4 = 24 suits per day for the second company. CHECK. - = 40.5 - 37.5 = 3 days. ! Correct !

Solved.

Answer by Theo(13342) (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.
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