One fashion house has to make 810 dresses and another one, 900 dresses during the same period of time. in the first house, the order was ready 3 days ahead of time and in the second house, 6 days ahead of time. how many dresses did each fashion house make a day if the second house made 21 dresses more a day than the first?
Description of variables : Wa = Original work rate of first fashion house
Wd = Original work rate of second fashion house .
Wb and Wc are the increased work rates of respective houses
Days = No of days reqd for completing work in original work rate of first house
Days 2 = No of days reqd for completing work in original work rate in 2nd house
Equations:
Wa * Days = 810 ---(i)
Wb * (Days -3) = 810 --(ii)
Wc * Days2 = 900 ---(iii)
Wd * (Days2 - 6) = 900 ---(iv)
second house made 21 dresses more a day than the first
Wd = Wb + 21 --(v)
Substituting Wb + 21 in place of Wd in (iv)
(Wb + 21) * (Days2 -6) = 900
(Days2 -6) = 900 / (Wb + 21)
from eqn (ii)
=> Wb * (Days -3) = 810 => Wb = 810 / (Days - 3)
from eqn (ii) we also get
=> Days = (810 / Wb ) + 3
From eqn(iv) Wd * (Days2 - 6) = 900 , we get
(Wb + 21 ) * (Days2 - 6) = 900
( ( 810 / (Days -3) + 21 ) * ( Days2 -6) = 900
So 900 = ( ( 810 / (Days -3) + 21 ) * ( Days2 -6)
From eqn(iv) we also get
Days2 = 900 / (Wb + 21) + 6
SOLVING :
Substituting 900 in eqn(iii)
Wc * Days2 = ( ( 810 / (Days -3) + 21 ) * ( Days2 -6) ) ) / (Days -3)
900 = ( ( ( 810 / (Days -3) + 21 ) * ( Days2 -6) ) / (Days -3)
Now i would bring in Wb in place of Days as I want to find Wb on solving the above equation
900= ( 810 ( Days2 -6) + 21 * (810 /Wb + 3) * (Days2 - 6 ) - 63( Days2 - 6) ) / ( (810 / Wb) + 3 - 3 )
Now like this i also substituted Days2 with Wb ,
So it stands like this
900= ( (729 * 10^3) / (WB + 21) + 17010/ Wb * ( 900/(Wb + 21) + 6 ) + 63 * ( 900 /(Wb + 21) + 6) - (102060 /Wb ) - 378 - 63 * ( 900/ (Wb + 21) + 6 ) + 378 ) / ( 810 / Wb)
10Wb / 9 = 729000 / (Wb + 21) + 15309000 / (Wb (Wb + 21) )
10Wb^3 + 210Wb^2 = 6561000Wb + 137781000
Wb = ...
Is the approach correct?
Description of variables : Wa = Original work rate of first fashion house
Wd = Original work rate of second fashion house .
Wb and Wc are the increased work rates of respective houses
Days = No of days reqd for completing work in original work rate of first house
Days 2 = No of days reqd for completing work in original work rate in 2nd house
Equations:
Wa * Days = 810 ---(i)
Wb * (Days -3) = 810 --(ii)
Wc * Days2 = 900 ---(iii)
Wd * (Days2 - 6) = 900 ---(iv)
second house made 21 dresses more a day than the first
Wd = Wb + 21 --(v)
Substituting Wb + 21 in place of Wd in (iv)
(Wb + 21) * (Days2 -6) = 900
(Days2 -6) = 900 / (Wb + 21)
from eqn (ii)
=> Wb * (Days -3) = 810 => Wb = 810 / (Days - 3)
from eqn (ii) we also get
=> Days = (810 / Wb ) + 3
From eqn(iv) Wd * (Days2 - 6) = 900 , we get
(Wb + 21 ) * (Days2 - 6) = 900
( ( 810 / (Days -3) + 21 ) * ( Days2 -6) = 900
So 900 = ( ( 810 / (Days -3) + 21 ) * ( Days2 -6)
From eqn(iv) we also get
Days2 = 900 / (Wb + 21) + 6
SOLVING :
Substituting 900 in eqn(iii)
Wc * Days2 = ( ( 810 / (Days -3) + 21 ) * ( Days2 -6) ) ) / (Days -3)
900 = ( ( ( 810 / (Days -3) + 21 ) * ( Days2 -6) ) / (Days -3)
Now i would bring in Wb in place of Days as I want to find Wb on solving the above equation
900= ( 810 ( Days2 -6) + 21 * (810 /Wb + 3) * (Days2 - 6 ) - 63( Days2 - 6) ) / ( (810 / Wb) + 3 - 3 )
Now like this i also substituted Days2 with Wb ,
So it stands like this
900= ( (729 * 10^3) / (WB + 21) + 17010/ Wb * ( 900/(Wb + 21) + 6 ) + 63 * ( 900 /(Wb + 21) + 6) - (102060 /Wb ) - 378 - 63 * ( 900/ (Wb + 21) + 6 ) + 378 ) / ( 810 / Wb)
10Wb / 9 = 729000 / (Wb + 21) + 15309000 / (Wb (Wb + 21) )
10Wb^3 + 210Wb^2 = 6561000Wb + 137781000
Wb = ...
Is the approach correct?