document.write( "Question 1059590: One alloy contains 3 times as much copper as silver. Another contains 5 times as much silver as copper. How much of each must be used to make 14kg in which there is twice as much copper as silver?\r
\n" ); document.write( "\n" ); document.write( "3c+s
\n" ); document.write( "5s+c
\n" ); document.write( "2c+s=14kg \n" ); document.write( "

Algebra.Com's Answer #674638 by ikleyn(52926) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "One alloy contains 3 times as much copper as silver. Another contains 5 times as much silver as copper.
\n" ); document.write( "How much of each must be used to make 14kg in which there is twice as much copper as silver?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "It is a standard mixture/alloy problem in a non-standard formulation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "First what I will do is to re-phrase it to the STANDARD formulation.\r\n" );
document.write( "It is done in three lines:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     First alloy is 25% silver.\r\n" );
document.write( "\r\n" );
document.write( "     The second alloy is , or % silver.\r\n" );
document.write( "     The resulting alloy is , or % silver.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now let \"x\" be an amount of the first alloy to be mixed, in kilograms,\r\n" );
document.write( "and let \"y\" be an amount of the first alloy to be mixed, in kilograms.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then your equations are \r\n" );
document.write( "\r\n" );
document.write( "x + y = 14,                         (1)   (for total amount)\r\n" );
document.write( " = .           (2)   (for the silver content)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify the system (1), (2). For it, multiply the both sides of (2) by 12. You will get\r\n" );
document.write( "\r\n" );
document.write( " x +   y = 14,                      (1')\r\n" );
document.write( "3x + 10y = 56.                      (2')\r\n" );
document.write( "\r\n" );
document.write( "To solve this system, express x = 14-y from (1') and substitute it into (2'). You will get a single equation for \"y\"\r\n" );
document.write( "\r\n" );
document.write( "3(14-y) + 10y = 56.\r\n" );
document.write( "\r\n" );
document.write( "From this point please complete the assignment on your own.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "There is entire bunch of lessons covering various types of mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - Mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - More Mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - Solving typical word problems on mixtures for solutions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for antifreeze solutions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for alloys \r
\n" ); document.write( "\n" ); document.write( "    - Typical word problems on mixtures from the archive\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution the mixture word problems.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook in the section \"Word problems\" under the topic \"Mixture problems\".\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The textbook contains many other solved word problems, as well as many other interesting and useful things.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );