Problem A

Cookies!

Benoit, Jin, Manuel, and Sarah shared a package of \(30\) cookies. After several days, all the cookies in the package were eaten by these four people and each person only ate whole cookies. Benoit recorded the following observations:

Sarah ate twice as many cookies as Jin.

Manuel ate two-thirds as many cookies as Sarah.

Benoit ate half as many cookies as Manuel.

Who ate the most cookies? Justify your answer.

What fraction of the number of cookies eaten by Sarah is the number of cookies eaten by Benoit? Justify your answer.

Who ate the fewest cookies? Justify your answer.

Someone ate \(6\) cookies. This was not the person who ate the most or fewest cookies. How many cookies did each person eat? Justify your answer.

**Theme:** Number Sense