document.write( "Question 163214: To the nearest tenth, how much pure acid must be added to 12 liters of a 20% acid solution in order to obtain a mixture that is 45% acid? \n" ); document.write( "

Algebra.Com's Answer #120247 by ptaylor(2198) $\"\"$ $\"About$

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\n" ); document.write( "Let x= amount of pure acid needed
\n" ); document.write( "Now we know that the amount of pure acid in the 20% solution (0.20*12)plus tha amount of pure acid added (x) has to equal the amount of pure acid in the final mixture ((12+x)*0.45). So our equation to solve is:
\n" ); document.write( "0.20*12+x=0.45(12+x) get rid of parens (distributive law) and simplify
\n" ); document.write( "2.4+x=5.4+0.45x subtract 0.45x and also 2.4 from each side
\n" ); document.write( "2.4-2.4+x-0.45x=5.4-2.4+0.45x-0.45x collect like terms\r
\n" ); document.write( "\n" ); document.write( "0.55x=3 divide each side by 0.55
\n" ); document.write( "x=5.5 liters\r
\n" ); document.write( "\n" ); document.write( "CK
\n" ); document.write( ".20*12+5.5=0.45*17.5
\n" ); document.write( "2.4+5.5=7.875
\n" ); document.write( "7.9~~~7.875\r
\n" ); document.write( "\n" ); document.write( "Maybe an easier way:
\n" ); document.write( "Amount of otherstuff in the 20% solution (0.80*12) plus the amount of otherstuff in the pure acid added(0) has to equal the amount of otherstuff in the final mixture (0.55(12+x)). So our equation to solve is:\r
\n" ); document.write( "\n" ); document.write( "0.80*12=0.55(12+x) get rid of parens and simplify
\n" ); document.write( "9.6=6.6+0.55x subtract 6.6 from each side\r
\n" ); document.write( "\n" ); document.write( "9.6-6.6=0.55x collect like terms
\n" ); document.write( "0.55x=3 -----------------same as before\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor\r
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