Question

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?

Answer 1

Answer:

By A 105 , By B 126

Step-by-step explanation:

Let two fashion houses are A and B and x be the time they have to make dresses

A has to make 810 dresses in in x days

B has to make 900 dresses in x days

For A order was ready x-3 days

For B order was ready x-6 days

Let A made y dresses in one day

B made y + 21 dresses in one day

to find the dresses made in one day by each fashion house?

Solution:

As

Total no of days taken = Total dress made / dresses made in one day

For A:

Total day = total dresses made / dresses made in one day

putting values

x-3 = $\frac{810}{y}$                          ....................(i)

For B:

Total day = total dresses made / dresses made in one day

putting values

x-6 = $\frac{900}{y+21}$                          ....................(ii)

Solving equation (i) for the value of x

we get

x = $\frac{810}{y}$ +3

putting this value in equation (ii)

$\frac{810}{y}$ +3 -6 = $\frac{900}{y+21}$

$\frac{810}{y} -3 = \frac{900}{y+21}$

cross multiplying

(810 -3y) (y +21) = 900y

810 y - 3$y^{2}$ + 17010 - 63 y = 900y

810y - 3$y^{2}$ + 17010 - 63 y -900y = 0

- 3$y^{2}$ - 153 y + 17010 = 0

taking (-1) common from equation gives

3$y^{2}$ + 153 y - 17010 = 0

dividing whole equation with 3

y^{2} + 51 y - 5670=0

midterm breaking of the equation gives us

y^{2} -105y + 54y - 5670=0

now taking common from the equation

y(y-105) + 54(y-105)=0

(y-105)(y+54)=0

Noe from this

either y-105 =0   or y + 54=0

so y= 105 or y= -54

As it is the No of suits so it could not be a negative number

so

Number of suits made by A is 105

Number of suits made by B is 105 +21 = 126

Answer 2

Answer:

The first house makes 54 dresses and second house makes 75 dresses in a day.

Step-by-step explanation:

Let the first house be House A

Let the second house be House B

Define x:

Let x be the number of days house A take

Number of days house B take = x - 3

Find the number of dresses each house can make in a day:

House A = 810/x

House B = 900/(x - 3)

Solve x:

House B makes 21 dress than House A in a day

900/(x - 3) - 810/x = 21

900x - 810(x - 3) = 21x(x - 3)

900x - 810x + 2430 = 21x² - 63x

90x + 2430 = 21x² - 63x

21x² - 153x - 2430 = 0

7x² - 51x - 810 = 0

(x - 15) (7x + 54) = 0

x = 15 or x = -54/7(rejected, since it is negative)

Find the number of dresses each house makes in a day:

House A = 810/x = 810/15  = 54 dresses

House B = 900/(x - 3) = 900/(15 - 3) = 75 dresses

Answer: The first house makes 54 dresses and second house makes 75 dresses in a day.