document.write( "Question 1195325: An alloy is made by melting and combining two or more metals. A metalsmith has two alloys, each containing different amounts of silver, that will be melted and combined to form another alloy. Every 10 grams of alloy A contains 2 grams of silver, and every 10 grams of alloy B contains 7 grams of silver. To obtain 100 grams of an alloy that contains 50 grams of silver, how many grams of alloy A should be combined with alloy B? \n" ); document.write( "

Algebra.Com's Answer #827789 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "An alloy is made by melting and combining two or more metals.
\n" ); document.write( "A metalsmith has two alloys, each containing different amounts of silver,
\n" ); document.write( "that will be melted and combined to form another alloy.
\n" ); document.write( "Every 10 grams of alloy A contains 2 grams of silver,
\n" ); document.write( "and every 10 grams of alloy B contains 7 grams of silver.
\n" ); document.write( "To obtain 100 grams of an alloy that contains 50 grams of silver,
\n" ); document.write( "how many grams of alloy A should be combined with alloy B?
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document.write( "Take x times 10 grams of alloy A and y times 10 grams of alloy B.\r\n" );
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document.write( "Then the total mass equation is\r\n" );
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document.write( "    10x + 10y = 100  grams    (1)\r\n" );
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document.write( "while the pure silver mass equation is\r\n" );
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document.write( "     2x +  7y =  50  grams.   (2)\r\n" );
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document.write( "So, you have this system of 2 equations for x and y\r\n" );
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document.write( "      x +   y = 10,    (1')\r\n" );
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document.write( "     2x +  7y = 50.    (2)\r\n" );
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document.write( "From eq(1'),  express  x = 10 - y  and substitute it into equation (2).  You will get\r\n" );
document.write( "a single equation for y\r\n" );
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document.write( "    2*(10-y) + 7y = 50\r\n" );
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document.write( "    20 - 2y  + 7y = 50\r\n" );
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document.write( "         5y       = 50 - 20\r\n" );
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document.write( "         5y       =    30\r\n" );
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document.write( "          y       =    30/5 = 6.\r\n" );
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document.write( "So, you should take 6*10 = 60 grams of alloy B and the rest, 100 - 60 = 40 grams of alloy A.   ANSWER\r\n" );
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document.write( "CHECK.  We check the content of silver. It is  7*6 + 4*2 = 42 + 8 = 50 grams.  ! Correct !\r\n" );
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