document.write( "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.
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Algebra.Com's Answer #854121 by ikleyn(53742) $\"\"$ $\"About$

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\n" ); document.write( "The Grand Master of the \"Noir et Lait\" Chocolaterie begins a signature production with 40 1/2 kg of raw chocolate base.
\n" ); document.write( "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
\n" ); document.write( "Batch Y is 2:1. Batch X is prepared as a high-intensity dark chocolate where the internal ratio of cocoa solids to sugar
\n" ); document.write( "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
\n" ); document.write( " $\"highlight%28cross%28minute%29%29\"$ mixture. To rectify the consistency, the chocolatier adds 5 3/4 kg of heavy cream to the remaining Batch X mixture.
\n" ); document.write( "Calculate:
\n" ); document.write( "(a) The final total mass of the Batch X mixture.
\n" ); document.write( "(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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\n" ); document.write( "\n" ); document.write( " Notice that I made editing in your post to restore the missed sense.\r
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\n" ); document.write( "\n" ); document.write( " Below is my solution to this edited/modified version.\r
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document.write( "                  S t e p   b y   s t e p\r\n" );
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document.write( "(1)  The starting mass is 40.5 kilogram.\r\n" );
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document.write( "     It is separated in two batches, X and Y, in proportion 2:1.\r\n" );
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document.write( "     Hence, mass X is 2/3 of 40.5 kg, or  27 kilograms,\r\n" );
document.write( "      while mass Y is 13.5 kilogram.\r\n" );
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document.write( "     We will work further with the mass X of 27 kilograms,\r\n" );
document.write( "     and the mass/amount Y is not interesting for us, anymore.\r\n" );
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document.write( "(2)  The mass X of 27 kilograms contains cocoa to sugar in proportion 8:1.\r\n" );
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document.write( "     Hence, mass X of 27 kilograms contains 24 kg of cocoa and 3 kg of sugar.\r\n" );
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document.write( "(3)  The mass X lost 2.25 kilograms due to the technological error.\r\n" );
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document.write( "     After that, X', the remaining part of mass X, is  27 - 2.25 = 24.75 kg.\r\n" );
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document.write( "     This remaining part of mass X  contains 8/9 * 24.75 = 22 kg of cocoa and  (24.75-22) = 2.75 kg of sugar.\r\n" );
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document.write( "(4)  To rectify the consistency, 5.75 kg of heavy cream was added.\r\n" );
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document.write( "     This addition did not affect the content of cocoa or sugar in mass X'.\r\n" );
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document.write( "(5)  After addition of 5.75 kg of heavy cream, the mass X''  is  (24.75 + 5.75) = 30.5 kilograms.\r\n" );
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document.write( "     It is the answer to question  (a).\r\n" );
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document.write( "     The answer to question (b) is this ratio   = 2 : 30 =  = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus, the problem is solved completely and both questions are answered.\r
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