document.write( "Question 993323: Adding 25 gallons of acid to a mixture, makes it 80% Acid solution, while adding 25 gallons of water makes it 60% Acid solution. What is the original acid percentage of the mixture? \n" ); document.write( "
Algebra.Com's Answer #612590 by josgarithmetic(39617)\"\" \"About 
You can put this solution on YOUR website!
You are not given the amount of original acid mixture, so give this a variable for its volume.
\n" ); document.write( "v, the initial volume in gallons of the starting mixture of unknown percent concentration.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let p be the percent concentration of your original acid mixture.
\n" ); document.write( "Additionally, you are forced to assume that your acid to add in pure form, the 100%, is a liquid.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "ADDING 25 GALLONS
\n" ); document.write( "\"%2825%2A100%2Bv%2Ap%29%2F%28v%2B25%29=80\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "ADDING 25 GALLONS OF WATER
\n" ); document.write( "\"%2825%2A0%2Bv%2Ap%29%2F%28v%2B25%29=60\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The system of equations slightly reworked is
\n" ); document.write( "\"system%28vp%2B2500=80%28v%2B25%29%2Cvp=60%28v%2B25%29%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "STEPS SOLVING THE SYSTEM
\n" ); document.write( "\"vp%2B2500=80v%2B8%2A25%2A10\"
\n" ); document.write( "\"vp%2B2500=80v%2B2000\"
\n" ); document.write( "\"vp%2B500=80v\"
\n" ); document.write( "\"vp-80v=-500\"
\n" ); document.write( "\"80v-vp=500\"
\n" ); document.write( "\"v%2880-p%29=500\"
\n" ); document.write( "\"highlight_green%28v=500%2F%2880-p%29%29\"
\n" ); document.write( "-
\n" ); document.write( "Next use the simpler, dilution equation.
\n" ); document.write( "\"%28500%2F%2880-p%29%29p=60%28%28500%2F%2880-p%29%29%2B25%29\"
\n" ); document.write( "\"500p%2F%2880-p%29=30000%2F%2880-p%29%2B1500\"
\n" ); document.write( "\"5p%2F%2880-p%29=300%2F%2880-p%29%2B15\"
\n" ); document.write( "\"p%2F%2880-p%29=60%2F%2880-p%29%2B3\"
\n" ); document.write( "\"p=60%2B3%2880-p%29\"
\n" ); document.write( "\"p=60%2B240-3p\"
\n" ); document.write( "\"4p=60%2B240\"
\n" ); document.write( "\"4p=300\"
\n" ); document.write( "\"p=300%2F4\"
\n" ); document.write( "\"highlight%28highlight%28p=75%29%29\"
\n" ); document.write( "
\n" ); document.write( "
\n" );