Question 1142738
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.