document.write( "Question 767867: the research department of a company that manufactures children's fruit drinks is experimenting with a new flavor. a 17.5% fructose solution is needed but only 10%and 20% solutions are available. How many Galons of the 10% fructose solution should be mixed with the 20% fructose solution to obtain 20 gallons of 17.5% fructose solution?
\n" ); document.write( "(please put the problem in system equation form which is {Ax+By=z
\n" ); document.write( " Gx+Hy=c before you compute them. thank you\r
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Algebra.Com's Answer #467893 by josgarithmetic(39618)\"\" \"About 
You can put this solution on YOUR website!
Account for the percent fructose wanted and used:
\n" ); document.write( "x for gallons 10% fructose, y for gallons of 20% fructose.
\n" ); document.write( "\"10x%2B20y=20%2A17.5\"
\n" ); document.write( "Notice the left and right sides being equated are the amount of fructose, as their mass (or weight). Simplifies if desired to :
\n" ); document.write( "\"x%2B2y=2%2A17.5\"
\n" ); document.write( "\"highlight%28x%2B2y=35%29\"\r
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\n" ); document.write( "\n" ); document.write( "Account for the amounts of solutions: Wanted is 20 gallons of fructose solution, so \"highlight%28x%2By=20%29\".\r
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\n" ); document.write( "\n" ); document.write( "The highlighted equations give you your system. Next is solve the system for x and y. One way is subtract the solution sum members from the percentage account members and solve first for y...
\n" ); document.write( "\"%28x%2B2y%29-%28x%2By%29=35-20\"
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\n" ); document.write( "ANOTHER DESCRIPTION TO DEVELOP THE PERCENT FRUCTOSE ACCOUNTING EQUATION:\r
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\n" ); document.write( "\n" ); document.write( "The available fructose solutions to be mixed are 10% and 20%, and what is wanted is 17.5% fructose.
\n" ); document.write( "Using x for the quantity of 10% fructose, and y for the quantity of 20% fructose, both x and y being in gallons, we can make a rational expression to represent the desired concentration.\r
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\n" ); document.write( "\n" ); document.write( "The amount of FRUCTOSE would be \"10%2Ax%2B20%2Ay\", and this is for only the fructose, as if without other materials, without any of the water.
\n" ); document.write( "The amount of mixed solution would be \"%28x%2By%29\"; in whatever units we have, in this case, \"%28x%2By%29\" GALLONS. The concentration in percent is then:\r
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\n" ); document.write( "\n" ); document.write( "\"%2810x%2B20y%29%2F%28x%2By%29=17.5\"\r
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\n" ); document.write( "\n" ); document.write( "We already know that we want 20 gallons of this 17.5% fructose solution, and that x+y=20. The rational equation is then this:\r
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\n" ); document.write( "\n" ); document.write( "\"%2810x%2B20y%29%2F20=17.5\"\r
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\n" ); document.write( "\n" ); document.write( "That should be simplified before working the steps for solving.
\n" ); document.write( "Instead of being in rational form, this should be transformed to an easier, more typical linear equation format. Other simplifications, too.\r
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\n" ); document.write( "\n" ); document.write( "\"10x%2B20y=%2817.5%29%2820%29\"________multplied left and right by 20.
\n" ); document.write( "\"x%2B2y=%2817.5%29%282%29\"___________divide left and right by 10.
\n" ); document.write( "\"highlight%28x%2B2y=35%29\"__________________simple multiplication computation.\r
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\n" ); document.write( "\n" ); document.write( "...and highlighted here is the best, simplest form of that equation to use.
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