document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154729>Question 1154729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Gabe​ Amodeo, a nuclear​ physicist, needs 60liters of a 40% acid solution. He currently has a 30 % solution and a 60 % solution. How many liters of each does he need to make the needed 6060 liters of 40% acid​ solution? </SPAN>\n" );
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document.write( "I'm assuming you meant to write \"60\" instead of \"6060\". \r<BR>\n" );
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document.write( "Gabe needs 60 liters of the 40% solution. This solution is a mix of water and pure acid. Specifically 60*0.4 = 24 liters of pure acid are needed. \r<BR>\n" );
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document.write( "Let <BR>\n" );
document.write( "x = amount of the 30% solution (in liters)<BR>\n" );
document.write( "y = amount of the 60% solution (in liters)\r<BR>\n" );
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document.write( "Based on those definitions above, we can say<BR>\n" );
document.write( "0.30x = amount of pure acid from the 30% mix<BR>\n" );
document.write( "0.60y = amount of pure acid from the 60% mix<BR>\n" );
document.write( "0.30x+0.60y = amount of pure acid in total<BR>\n" );
document.write( "0.30x+0.60y = 24, since Gabe wants 24 liters of pure acid in the end\r<BR>\n" );
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document.write( "At the same time, we can also say x+y = 60 because the two individual solution amounts (x and y) will combine to the overall amount of solution of 60 liters. Solve for y to get y = 60-x\r<BR>\n" );
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document.write( "Plug this into 0.30x+0.60y = 24, and solve for x\r<BR>\n" );
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document.write( "0.30x+0.60y = 24<BR>\n" );
document.write( "0.30x+0.60( y ) = 24<BR>\n" );
document.write( "0.30x+0.60( 60-x ) = 24 ... replace y with 60-x<BR>\n" );
document.write( "0.30x+0.60(60)+0.60(-x) = 24 ... distribute<BR>\n" );
document.write( "0.30x+36-0.60x = 24<BR>\n" );
document.write( "-0.30x+36 = 24<BR>\n" );
document.write( "-0.30x+36-36 = 24-36 ... subtract 36 from both sides<BR>\n" );
document.write( "-0.30x = -12<BR>\n" );
document.write( "-0.30x/(-0.30) = -12/(-0.30) .... divide both sides by -0.30<BR>\n" );
document.write( "x = 40<BR>\n" );
document.write( "We need <font color=red size=4>40 liters</font> of the 30% solution\r<BR>\n" );
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document.write( "y = 60-x<BR>\n" );
document.write( "y = 60-40<BR>\n" );
document.write( "y = 20<BR>\n" );
document.write( "and <font color=red size=4>20 liters</font> of the 60% solution\r<BR>\n" );
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document.write( "With those x and y values in mind, note that<BR>\n" );
document.write( "30% of x = 30% of 40 = 0.30*40 = 12<BR>\n" );
document.write( "60% of y = 60% of 20 = 0.60*20 = 12<BR>\n" );
document.write( "Those values sum to 12+12 = 24, which was the amount of pure acid Gabe needs. <BR>\n" );
document.write( "This helps confirm we have the right answer.\r<BR>\n" );
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document.write( "Answers: <BR>\n" );
document.write( "<font color=red size=4>40 liters</font> of the 30% solution<BR>\n" );
document.write( "<font color=red size=4>20 liters</font> of the 60% solution<BR>\n" );
document.write( "</font> </SPAN>\n" );
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