GMAT, GRE Mixture Problem

A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?

A. 1.5
B. 2.5
C. 3
D. 4.5
E. 5





Removing cups of sauce means we're removing parts of both chocolate and puree.

We have 15 cups of sauce. The prompt asks us to remove "X" amount of cups from the sauce, and add the same "X" amount of chocolate to give us an equal 7.5/7.5 split. We're not splitting the "X" amount.  

In Choice B, if we take 2.5 out of 15 ... we have 12.5 cups of Sauce: giving us 5 cups of Chocolate and 7.5 cups of Puree (since we have to take 40% choc. and 60% Puree from the sauce)
Now, adding the same amount, 2.5 back into the Chocolate, we have the perfect split: 7.5/7.5 ... Hence, B is correct.

We have 15 cups of Sauce
6 Chocolate and 9 Puree.
Focus on the Chocolate. We need to raise its initial value UP to 7.5 by removing cups of the sauce and replacing the same amount with cups of chocolate. 

Now, to get 7.5, we need to remove "X" amount of the 15 cups of sauce and MULTIPLY that value by 40% --- giving us the chocolate value of the "reduced" sauce value.  
Just like we earlier with Choice B: (15-2.5)(2/5) = 5

Then, we need to add the same "X" amount back into the chocolate. And, that's how we get

7.5 = 2/5 (15 - X) + X 
7.5 = 6 - .4X + X
1.5 = .6X
X = 2.5

B