document.write( "Question 1054315: Two mixtures contain p% and q% respectively of a certain ingredient. Show x units of the first is combined with y units of the second so the resulting mixture is r% of the ingredient.\r
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Algebra.Com's Answer #669532 by ikleyn(52872) $\"\"$ $\"About$

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\n" ); document.write( "Two mixtures contain p% and q% respectively of a certain ingredient. Show x units of the first is combined with y units
\n" ); document.write( "of the second so the resulting mixture is r% of the ingredient.\r
\n" ); document.write( "\n" ); document.write( "Unsure how to proceed. Thanks again.
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document.write( "The correct question should be:\r\n" );
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document.write( "     \"how x units of the first is combined with y units \r\n" );
document.write( "      of the second so the resulting mixture is r% of the ingredient?\"\r\n" );
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document.write( "In other words, you are asked to find the ratio of \"x\" to \"y\" that provides r% concentration of the mixture.\r\n" );
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document.write( "The \"concentration\" equation is\r\n" );
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document.write( "px + qy = r(x+y).   (1)\r\n" );
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document.write( "The values \"p\", \"q\" and \"r\" are given; the ratio  is under the question.\r\n" );
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document.write( "Based on the equation (1), collect the terms with x on the left and the therms with y on the right:\r\n" );
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document.write( "px - rx = ry - qy,   or\r\n" );
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document.write( "(p-r)x = (r-q)y.\r\n" );
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document.write( "It gives you\r\n" );
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document.write( " = .\r\n" );
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document.write( "Thus you found the ratio . \r\n" );
document.write( "The problem is solved.\r\n" );
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document.write( "By the way, the solution does exist if and only if  \"r\"  lies between the values of \"p\"  and  \"q\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "There is entire bunch of the 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 dry substances like coffee beans, nuts, cashew and peanuts\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for dry substances like candies, dried fruits\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on mixtures for dry substances like soil and sand\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
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\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution the mixture word problems.\r
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\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
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\n" ); document.write( "\n" ); document.write( "It contains many other solved word problems, as well as many other interesting and useful things.\r
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