document.write( "Question 1158751: 1. Mixture Problem
\n" ); document.write( "A grocer mixes peanuts that cost $1.49 per pound and walnuts that cost $2.69 per pound to make
\n" ); document.write( "100 pounds of a mixture that costs $2.21 per pound. How much of each kind of nut is put into the
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\n" ); document.write( "2. Mixture Problem
\n" ); document.write( "How much water must be evaporated from 80 pounds of a 12% solution of salt in order to obtain a
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\n" ); document.write( "3. Investment Problem
\n" ); document.write( "A man invested Php 6,000, part of it at 3% and the rest at 4%. The total annual income from the
\n" ); document.write( "two investments is Php 208. How much is invested at each of these rates?
\n" ); document.write( "4. Pattern Problem
\n" ); document.write( "Determine the next number in the sequence 0, 10, 24, 56, 112, 190, ...
\n" ); document.write( "5. Pattern Problem
\n" ); document.write( "One cut of a stick of licorice produces two pieces. Two cuts produce three pieces. Three cuts
\n" ); document.write( "produce four pieces.
\n" ); document.write( "a. How many pieces are produced by five cuts and by six cuts?
\n" ); document.write( "b. Predict the nth-term formula for the number of pieces of licorice that are produced by n cuts
\n" ); document.write( "of a stick of licorice. \n" ); document.write( "

Algebra.Com's Answer #781733 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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ONE and ONLY ONE problem/question per post.

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\n" ); document.write( "\n" ); document.write( "I will solve only one problem for you.\r
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\n" ); document.write( "\n" ); document.write( "2. Mixture Problem
\n" ); document.write( "How much water must be evaporated from 80 pounds of a 12% solution of salt in order to obtain a 20% solution?\r
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document.write( "Let W be the MASS of water to evaporate, in pounds.\r\n" );
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document.write( "The amount of salt in the original 80 pounds of the 12% solution was  0.12*80 = 9.6 pounds.\r\n" );
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document.write( "When W pounds of water were evaporated, the remaining mass became  80 pounds - W pounds.\r\n" );
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document.write( "We want the new salt concentration be 20%.  It means\r\n" );
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document.write( "     = 0.2.   (1)\r\n" );
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document.write( "(Notice that when the water evaporates, the mass of salt REMAINS the SAME (!) )\r\n" );
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document.write( "To solve equation (1), multiply both sides by (80-W).  You will get\r\n" );
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document.write( "    9.6 = 0.2*(80-W).\r\n" );
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document.write( "Simplify and find W.\r\n" );
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document.write( "    9.6 = 0.2*80 - 0.2W\r\n" );
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document.write( "    0.2W = 0.2*80 - 9.6 = 6.4,\r\n" );
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document.write( "    W =  = 32 pounds.\r\n" );
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document.write( "ANSWER.  32 pounds of water should be evaporated.\r\n" );
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document.write( "CHECK.  I will check equation  (1) for the concentration\r\n" );
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document.write( "         =  = 0.2,  which is precisely correct (!)\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a standard and typical mixture problem.\r
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\n" ); document.write( "\n" ); document.write( "In this site, there is a bunch of lessons, covering various types of mixture problems. See introductory lessons\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
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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( "The referred lessons are the part of this online textbook under the topic \"Mixture problems\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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