document.write( "Question 333567: A chemist needs 5 liters of a 70% alcohol solution. If she mixes a 90% alcohol solution and a 40% alcohol solution, how much of the 40% solution should she use? \n" ); document.write( "

Algebra.Com's Answer #239103 by jrfrunner(365) $\"\"$ $\"About$

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let N=amount of 90% solution
\n" ); document.write( "let F=amount of 40% solution
\n" ); document.write( "---
\n" ); document.write( "given:
\n" ); document.write( "equation 1) Amount of solution: N+F=5
\n" ); document.write( "equation 2) Amount of alcohol: 0.9*N+0.4*F=0.7*5=3.5
\n" ); document.write( "--
\n" ); document.write( "you now have two equations and two unknowns, so should be able to solve
\n" ); document.write( "--
\n" ); document.write( "solve equation 1, for either N, or F: N=5-F
\n" ); document.write( "substitute N=5-F into second equation
\n" ); document.write( "0.9*N+0.4*F=3.5
\n" ); document.write( "0.9*(5-F)+0.4*F=3.5
\n" ); document.write( "9(5-F)+4*F=35 (multiply both sides by 10 to work with whole numbers)
\n" ); document.write( "45-9F+4F=35
\n" ); document.write( "45-4F=35
\n" ); document.write( "45-35=4F
\n" ); document.write( "10=5F
\n" ); document.write( "2=F
\n" ); document.write( "and since N=5-F then N=5-2=3
\n" ); document.write( "--
\n" ); document.write( "validate answers F=2, N=3
\n" ); document.write( "go back to original equations and subsitute this values to see if they are correct
\n" ); document.write( "--
\n" ); document.write( "N+F=5: 2+3=5 check
\n" ); document.write( "0.9*N+0.4*F=3.5: 0.9*3+0.4*2 = 2.7+0.8=3.5 check \n" ); document.write( "

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