Question

A bakery made some cookies. 1/2 of the cookies were placed in large boxes. 3/7 of the cookies were placed in small boxes . The remaining cookies were kept in a refrigerator. There were 7 large boxes and 18 small boxes of cookies. Each large box contained 32 more cookies than each small box.

Answer 1

Answer:

378 cookies

Step-by-step explanation:

Let total amount of cookies be y

Let amount of cookies in each small box = x

let amount of cookies in each large box = x + 32

Therefore total amount of cookies in 18 small boxes = 18x

Total amount of cookies in 7 large boxes = 7(x+18) = 7x + 126

Fractional amount of cookies in small & large boxes = 1/2 + 3/7 = 13/14

Total amount of cookies in  small & large boxes = 18x + 7x + 126 = 25x + 126

Fractional amount of small cookies equals amount of small cookies in 18 boxes.

3/7y = 18x------------------Eqn 1

From eqn above y = 42x

Equating fractional sum & total sum =

25x + 126 = (13/14)y

Upon cross multiplication

350x + 1764 = 13y---------Eqn 2

Substituting y = 42x into equation 2

350x +1764 = 13(42x)

1764 = 546x - 350x

1764 = 196x

x = 9 cookies

Therefore total number of cookies = 42 × 9 = 378 cookies