Four hungry boys went to bed, thinking about the batch of cookies that their mot

Question

Four hungry boys went to bed, thinking about the batch of cookies that their mother had just baked. In the middle of the night, each of them got up and ate some of the cookies. Adam got up first. He gave a cookie to the dog, then ate 1/8 of the remaining cookies and went back to bed. Billy was the next to get up, and he ate 1/7 of the cookies. (The dog didn’t get any from him because he thought the dog looked full.) Charlie then got up and gave 3 cookies to the dog. Then he ate 1/5 of the remaining cookies. Daniel was the last to get up, and he ate just 6 cookies. (He offered one to the dog, but the dog just turned away with a decided grimace.) When their mother went into the kitchen the next morning, she found ants, a pale-looking dog, a lot of crumbs, and only a few cookies, so she quickly whipped up another small batch to increase the amount by 3/5. Then she had a total of 48 cookies. How many cookies had she baked the day before?

Explanation / Answer

Starting from 48, we have to proceed backward to find out the number of cookies

(1+3/5)p = 48

p = 48x5/8 = 30

30+6 (by Daniel) = 36

(q - 3)x4/5 = 36

q = 48

r x (1-1/7) = 48

r = 48x7/6 = 56

(s - 1)x7/8 = 56

s = 65

So, she had baked a total of 65 cookies on the day before.

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