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# algebra

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Homer is giving some cookies to each of his three brothers. To the oldest, he gives half of the cookies and half a cookie. He then gives half of what is now left and half a cookie to his second brother. Finally, he gives half of what is now left and half a cookie to his second brother. At no time is a cookie broken or cut. How many cookies did Homer have to begin with?

May 7, 2021

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Homer is giving some cookies to each of his three brothers. To the oldest, he gives half of the cookies and half a cookie. He then gives half of what is now left and half a cookie to his second brother. Finally, he gives half of what is now left and half a cookie to his third brother. At no time is a cookie broken or cut. How many cookies did Homer have to begin with?

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IF Homer had 100 cookies, he would give 50.5 cookies to his oldest brother, 25.25 to his second brother, and 12.625 to his third brother.

The ratio of given cookies is as follows:   50.5 : 25.25 : 12.625     or     4 : 2 : 1

So, Homer had 7 cookies, and he gave them all to his brothers:

Oldest          3.5 + .5 = 4

Second        1.5 + .5 = 2

Third              .5 + .5 = 1

No cookie needed to be broken!

May 17, 2021