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
