vaishnogmat 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
Responding to a pm:
Quote:
Using the Scale method
40% 50% 100%
15-x x
Hence
(15-x)/x = 50/10
I cannot understand how 15- x cups can be equal to 40% of chocolate . where X is the cups of Mixture removed and replaced with Pure Chocolate.
My understanding:
The 15 cups are prepared by mistaken proportions of 40% chocolate and 60% Rasberry . Hence when we remove x cups of mixture from 15 cups of Chocolate + Rasberry Mixture , we are left with chocolate equal to 40% of 15-x
Hence now 40%* ( 15-x) Choco will be mixed with x cups of Choco at 100% to obtain choco at 50%
Is this understanding correct?
Will the concentration of chocolate always be at 40% ,in the 15 Cups prepared by mistaken combination , even if we consider 1 cup or 2 cups or x cups of the mixture?
Yes, we assume that the mix is homogeneous. Otherwise, we will not be able to solve the question.
Look at the question from a different perspective for ease (don't mix it up with algebra):
You have 15 cups of sauce with 40% chocolate. You also have unlimited amount of pure chocolate sauce. Now you need to mix these two in such a way that you get total 15 cups of sauce with 50% chocolate.
Using scale method:
w1/w2 = (100 - 50)/(50 - 40) = 5/1
w1 - Amount of 40% chocolate sauce
w2 - Amount of pure chocolate sauce
So for every 5 cups of 40% chocolate sauce, we need 1 cup of pure chocolate sauce. This will give us 6 cups of 50% chocolate sauce. But we need 15 cups of 50% chocolate sauce.
So we need to mix 5*15/6 = 12.5 cups of 40% chocolate sauce with 1*15/6 = 2.5 cups of pure chocolate sauce.
Hence, when we are replacing, we remove 2.5 cups of 40% chocolate sauce and put 2.5 cups of pure chocolate in it.
Answer (B)
Look at example 1 here:
http://www.veritasprep.com/blog/2012/01 ... -mixtures/It is very similar to this question.