There are three kinds of cookies in a cookie jar: chocolate chip, peanut butter and oatmeal. If the number of oatmeal cookies is 2/3 the number of chocolate chip cookies and the number of chocolate chip cookies is 3/7 the number of peanut butter cookies, what fraction of the cookies are oatmeal?

Question

anonymous · Answer

You want to set up your system of equations.  Use $c$, $p$, and $o$ as variables to represent the numbers of chocolate chip, peanut butter, and oatmeal cookies respectively.

What algebraic expressions can you get?

anonymous · Answer

"the number of oatmeal cookies is 2/3 the number of chocolate chip cookies"
expresses an equation for variables $o$ and $c$.

anonymous · Answer

"the number of chocolate chip cookies and the number of chocolate chip cookies is 3/7 the number of peanut butter cookies"
this gives you another equation

anonymous · Answer

o=2/3c   c=3/7p  p=7/2o

anonymous · Answer

Now, just by common sense we know the total number of cookies is $c + o + p$.

anonymous · Answer

You want to use the equations you wrote down to change the terms $o$ and $p$ into terms of $c$.

anonymous · Answer

For example: $$
c + o + p = c+\left( \frac{2}{3} c \right) + p
$$because $ \large o = \frac{2}{3} c$

anonymous · Answer

@ArkGoLucky   Do you understand?

anonymous · Answer

do I have to solve for all the variables?

anonymous · Answer

So: $$
c+o+p= 1
$$because the total cookies is 1 times the total cookies.

anonymous · Answer

No, you just need to get everything in terms of c

anonymous · Answer

wio, please forgive the interuption, but I saw your formula, and I suck at math... but i think i figured out the answer... do you mind if i stick around to see if im right?

anonymous · Answer

@Lurch   No problem.

anonymous · Answer

thanks!

anonymous · Answer

So if I solve everything in terms of c, how does that help me find o

anonymous · Answer

oooh, I see what you mean.... nevermind, get it all in terms of $o$.

anonymous · Answer

crap... I was wrong.... back to the scratch paper...

anonymous · Answer

and also, why does c+p+o=1 aren't o, c, p the number of cookies

anonymous · Answer

you're right... I was thinking a bit too far ahead...what I should have said is: $$
c+p+o = n
$$Where $n$ is the total number of cookies.

What we want is to find $o=??? n$.  We use the fact that $n = c+p+o$.

anonymous · Answer

is the answer 1/6

anonymous · Answer

@ArkGoLucky Just did the problem, and that is what I got.

anonymous · Answer

okay thanks for the help

anonymous · Answer

@ArkGoLucky http://www.wolframalpha.com/input/?i=o+%3D+%282%2F3%29c%2C+c+%3D+%283%2F7%29p%2C+c+%2B+p+%2B+o+%3D+n%2C+b+%3D+o%2Fn Here is proof that you are correct. I make another variable $b$ which was equal to $o/n$. Wolfram said $b = 1/6$.

anonymous · Answer

thank you. It feels good to be right