Question

One fashion house has to make 810 dresses and another one 900 dresses during the same period of time. In the fist 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 fist?

Answer 1

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.