document.write( "Question 1203490: Sornog is an alloy composed of gold and tustrite, but contains no motrium. Suppose yotril is an alloy that is composed of 75% gold, 13% tustrite, and 12% motrium. To make a trophy for a contest, some sornog is combined with some yotril to produce a trophy that is 72% gold, 20% tustrite, and 8% motrium. What is the percentage of gold in the sornog that was used to make the trophies? \n" ); document.write( "

Algebra.Com's Answer #839137 by ikleyn(52908) $\"\"$ $\"About$

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\n" ); document.write( "Sornog is an alloy composed of Gold and Tustrite, but contains no Motrium.
\n" ); document.write( "Suppose Yotril is an alloy that is composed of 75% Gold, 13% Tustrite, and 12% Motrium.
\n" ); document.write( "To make a Trophy for a contest, some Sornog is combined with some Yotril to produce a Trophy
\n" ); document.write( "that is 72% Gold, 20% Tustrite, and 8% Motrium.
\n" ); document.write( "What is the percentage of Gold in the Sornog that was used to make the Trophy?
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\n" ); document.write( "\n" ); document.write( "        From one point of view, this problem is partly joke and partly entertainment.\r
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\n" ); document.write( "\n" ); document.write( "        From the other side, the solution assumes that the reader is a mature person
\n" ); document.write( "        in solving mixture problems and has enough developed common sense or experience
\n" ); document.write( "        to understand the solution below.\r
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document.write( "The mass percentage formulas for participating materials are\r\n" );
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document.write( "    Sornog = (x   g,  y   t,  0   m)\r\n" );
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document.write( "    Yotril = (0.75g,  0.13t,  0.12m)\r\n" );
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document.write( "    Trophy = (0.72g,  0.20t,  0.08m)\r\n" );
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document.write( "         Here letters g, t, and m designate gold, Tustrite and Motrium, as elementary components;\r\n" );
document.write( "         x and y symbolize the quantities. \r\n" );
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document.write( "We combine \"a\" grams of Sornog and \"b\" grams of Yotril and get a+b grams of Trophy.\r\n" );
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document.write( "Looking for the Motrium component, we see that \r\n" );
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document.write( "    0*a + 0.12b = 0.08(a+b),\r\n" );
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document.write( "or, simplifying\r\n" );
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document.write( "    0.12b = 0.08a + 0.08b  --->  0.12b - 0.08b = 0.08a  --->  0.04b = 0.08a  --->  b = 2a.\r\n" );
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document.write( "It tells us that \"a\" grams of the Sornog and 2a grams of the Youtril were melted to get a+2a = 3a grams of the Trophy.\r\n" );
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document.write( "Having this, we can write the mass equation for the gold components\r\n" );
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document.write( "    ax + (2a)*0.75 = (3a)*0.72.\r\n" );
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document.write( "From it, we express \"x\"\r\n" );
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document.write( "    x =  = 3*0.72-2*0.75 = 0.66.\r\n" );
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document.write( "It tells us that the percentage of gold in the used Sornog is 66%.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( " So, this problem is a joke and entertainment problem for specialists.\r
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\n" ); document.write( "\n" ); document.write( "At the school level, it is accessible only for those advanced students,
\n" ); document.write( "who are able (are trained) to solve problems of a Math Olympiad level.\r
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