One night in the Carsons household Mrs Carson made a batch o

One night, in the Carson\'s household, Mrs. Carson made a batch of cookies for herself and her four children. They each had one cookie before they went to bed that night. In the middle of the night, each of them got up and ate some cookies. Freddie got up first. He separated the cookies into three piles and found there was one left over. He gave the leftover cookie to the dog, Buster, and then ate 1/3 of the remaining cookies and went back to bed. Rhonda was next to get up, and she ate 1/4 of the cookies. (Buster didn\'t get any from her). Chad then got up and gave 2 cookies to the dog. Then he ate 1/5 of the remaining cookies. Martha was the last to get up, and she ate just 4 cookies and then gave 1 to Buster. When their mother, Paula, went into the kitchen the next morning, she found only 15 cookies. How many had she originally baked?

Solution

Let total cookies she originally baked = x

Now Fredie eaten part = 1/3 of (x-1) =(x-1)/3 (as 1 cookie was given to Buster.

Now remaining amount for Rhonda= 2(x-1)/3 and as she ate its 1/4 , so total amount for Chad = (1/4)(2(x-1)/3)

=(x-1)/6

Now remaining amount for Chad = (x-1)6-2 =(x-1-12)/6 ( as she gave 2 to dog)

and eaten cookies by Chad = (x-13)/6(5)= (x-13)/30

So remaining cookies = 4(x-13)/6 = 2(x-13)/3

And lastly remaining cookies = 2(x-13)/3-5 = (2x-26 -15)/3 = (2x- 41)/3   

(It is because 1 was given to buster and 4 were eaten by Martha)

and this last amount is equal to 15.

so (2x-41)/3= 15

2x-41= 15(3)= 45

2x=45+41= 86

x= 86/2= 43

and four cookies these four children already had in the beginning.

So total cookies that she cooked = 43+4 = 47

Answer