russ9 wrote:
blueseas wrote:
vaishnogmat wrote:
Q) 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
we have 15 cups os sauce with \(40 %\) choc and \(60 %\) rasb
cups of choc = \(0.4*15 = 6\)
cups of rasb = \(0.6*15 = 9\)
now let say we removed x cup of original mix and replaced with x cups of choc.
therefore final number of cups of choc =\(6-0.4x+x\)
now this number of cup should be 50% of total = \(15/2 = 7.5\)
therefore \(6-0.4x+x= 7.5\)
on solving \(x= 2.5\)
hence B
Hi,
I was with you until " final number of cups of choc =\(6-0.4x+x\)"
After I came up with 6 and 9, i proceeded to divide the options in half. What I mean is, for option B, 2.5 -- if we removed 2.5, that means that we would remove half of the 2.5 = 1.25 of chocolate and 1.25 of puree. I'm not sure why you removed 40%(although I can see that 40% represents the chocolate percent). Logically, if we remove the sauce, wouldn't we remove equal parts of puree and equal parts of chocolate?
Hi, There! I guess I'm a few months too late on this response, but I'll try to give it a go.
When we remove cups of the sauce, we're removing parts of both chocolate and puree --- according to their respective percentages.
In this case: 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. For 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.
Now, how did we get there through the method you tried to follow?
First of all, let's think logically: we have 15 cups of Sauce, broken down to as you pointed out, 6 Chocolate and 9 Puree.
Focus only 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 this equation:
7.5 = 2/5 (15 - X) + X
7.5 = 6 - .4X + X
1.5 = .6X
X = 2.5
A good problem, for good practice. Hope that helped!