Question 1210588: The Grand Master of the "Noir et Lait" Chocolaterie begins a signature production with 40 1/2 kg of raw chocolate base. He divides this base into two separate batches, X and Y, such that the ratio of the mass of Batch X to the mass of Batch Y is 2:1. Batch X is prepared as a high-intensity dark chocolate where the internal ratio of cocoa solids to sugar is exactly 8:1. However, during the tempering process, a technical error leads to the loss of 2 1/4 kg of the Batch X minute. To rectify the consistency, the chocolatier adds 5 3/4 kg of heavy cream to the remaining Batch X mixture.
Calculate:
1. The final total mass of the Batch X mixture.
2. The simplified fraction representing the ratio of the sugar's mass to the total final mass of the Batch X mixture.
Answer by ikleyn(53742)   (Show Source):
You can put this solution on YOUR website! .
The Grand Master of the "Noir et Lait" Chocolaterie begins a signature production with 40 1/2 kg of raw chocolate base.
He divides this base into two separate batches, X and Y, such that the ratio of the mass of Batch X to the mass of
Batch Y is 2:1. Batch X is prepared as a high-intensity dark chocolate where the internal ratio of cocoa solids to sugar
is exactly 8:1. However, during the tempering process, a technical error leads to the loss of 2 1/4 kg of the Batch X
 mixture. To rectify the consistency, the chocolatier adds 5 3/4 kg of heavy cream to the remaining Batch X mixture.
Calculate:
(a) The final total mass of the Batch X mixture.
(b) The simplified fraction representing the ratio of the sugar's mass to the total final mass of the Batch X mixture.
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Notice that I made editing in your post to restore the missed sense.
Below is my solution to this edited/modified version.
S t e p b y s t e p
(1) The starting mass is 40.5 kilogram.
It is separated in two batches, X and Y, in proportion 2:1.
Hence, mass X is 2/3 of 40.5 kg, or 27 kilograms,
while mass Y is 13.5 kilogram.
We will work further with the mass X of 27 kilograms,
and the mass/amount Y is not interesting for us, anymore.
(2) The mass X of 27 kilograms contains cocoa to sugar in proportion 8:1.
Hence, mass X of 27 kilograms contains 24 kg of cocoa and 3 kg of sugar.
(3) The mass X lost 2.25 kilograms due to the technological error.
After that, X', the remaining part of mass X, is 27 - 2.25 = 24.75 kg.
This remaining part of mass X contains 8/9 * 24.75 = 22 kg of cocoa and (24.75-22) = 2.75 kg of sugar.
(4) To rectify the consistency, 5.75 kg of heavy cream was added.
This addition did not affect the content of cocoa or sugar in mass X'.
(5) After addition of 5.75 kg of heavy cream, the mass X'' is (24.75 + 5.75) = 30.5 kilograms.
It is the answer to question (a).
The answer to question (b) is this ratio  = 2 : 30 =  =  .
Thus, the problem is solved completely and both questions are answered.
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