SOLUTION: 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?

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?
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
let N=amount of 90% solution
let F=amount of 40% solution
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given:
equation 1) Amount of solution: N+F=5
equation 2) Amount of alcohol: 0.9*N+0.4*F=0.7*5=3.5
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you now have two equations and two unknowns, so should be able to solve
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solve equation 1, for either N, or F: N=5-F
substitute N=5-F into second equation
0.9*N+0.4*F=3.5
0.9*(5-F)+0.4*F=3.5
9(5-F)+4*F=35 (multiply both sides by 10 to work with whole numbers)
45-9F+4F=35
45-4F=35
45-35=4F
10=5F
2=F
and since N=5-F then N=5-2=3
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validate answers F=2, N=3
go back to original equations and subsitute this values to see if they are correct
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N+F=5: 2+3=5 check
0.9*N+0.4*F=3.5: 0.9*3+0.4*2 = 2.7+0.8=3.5 check
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