A dessert recipe calls for 50% melted chocolate and 50%

BTGmoderatorDC wrote: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

OA B

Source: Veritas Prep

We are given that a chef makes 15 cups of sauce with 40% melted chocolate, or 15 x 0.4 = 6 cups of melted chocolate, and 60% raspberry puree, or 0.6 x 15 = 9 cups of raspberry puree. We need to determine how many cups of the sauce he needs to remove and replace with pure melted chocolate to make the sauce 50% of each. In order to have 50% of each, we want 7.5 cups of melted chocolate and 7.5 cups of raspberry puree. We can let n = the number of cups of sauce removed and also the number of cups of pure melted chocolate added.

Recall that we have 6 cups of melted chocolate in the sauce (which is 40% of the sauce). If we remove n cups of sauce, we are actually removing 0.4n cups of melted chocolate. Since we are adding back n cups of pure melted chocolate, the number of cups of melted chocolate will increased by n, and we want the end result to be 7.5 cups of melted chocolate. Thus, we can create the following equation to solve for n:

6 - 0.4n + n = 7.5

0.6n = 1.5

n = 1.5/0.6 = 15/6 = 2.5

Answer: B