Problem 170

Solution 1
We will simulate the process in steps.
In the beginning, we have:

$4$ ounces of coffee in cup $1$
$4$ ounces of cream in cup $2$
In the first step we pour $4/2=2$ ounces of coffee from cup $1$ to cup $2$, getting:

$2$ ounces of coffee in cup $1$
$2$ ounces of coffee and $4$ ounces of cream in cup $2$
In the second step we pour $2/2=1$ ounce of coffee and $4/2=2$ ounces of cream from cup $2$ to cup $1$, getting:

$2+1=3$ ounces of coffee and $0+2=2$ ounces of cream in cup $1$
the rest in cup $2$
Hence at the end we have $3+2=5$ ounces of liquid in cup $1$, and out of these $2$ ounces is cream. Thus the answer is $\boxed{\text{(D) } \frac 25}$.

Solution 2
Let's consider this in steps.
We have 4 ounces of coffee in the first cup.
We hace 4 ounces of cream in the second cup.
We take half of the coffee in the first cup(2 ounces), and add it to the second cup, yielding 6 ounces in total in the second cup(in a 1:2 ratio between coffee and cream, respecitvely).
We then take half of the second cup and pour it into the first cup. $6/2=3$, so there is now 5 ounces in the first cup, 2 coffee and 3 the mixture.
Remember that the mixture is in a 1:2 ratio between coffee and cream. So, coffee has one ounce and cream has 2 ounces.
In total, there is 2 ounces in the 5 ounce first cup. Putting 2 over 5, we get the answer. Therefore, the answer is $\boxed{\text{(D) } \frac 25}$.
~MathKatana