8th grade math problem? please help? 10 points!
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8th grade math problem? please help? 10 points!

[From: ] [author: ] [Date: 11-11-13] [Hit: ]
can anyone please help me? thanks in advance!a lab technician has 20% of alchohol solution and a 40% alchohol solution. He wants to make 75 gallons of a 36% alchohol solution. how much of EACH solution should he use? use either eleiminition or susbistuation to solve this problem.......
i've been working FOREVER on this qestion, and i keep getting really long decimal anwsers which i think are wrong. so i'm kinda giving up on this :(
can anyone please help me? thanks in advance! 10 points to best anwser

a lab technician has 20% of alchohol solution and a 40% alchohol solution. He wants to make 75 gallons of a 36% alchohol solution. how much of EACH solution should he use? use either eleiminition or susbistuation to solve this problem.

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Let x and (75-x) gallons of 20% and 40% alcohol solutions be mixed to produce 75 gallons of 36% alcohol.

Then the alcohol concentrations satisfy

(20% of x) +[40% of (75-x)]=(36% of 75)

i.e., (20/100)(x) + (40/100)(75-x) =(36/100)(75)

i.e., 0.2x +0.4(75-x) =0.36(75)

i.e., 0.2x+30-0.4x=27
i.e., x=15

Thus, 15 gallons of 20%alcohol and (75-15)=60 gallons of 40% solutions are required to prepare 75 gallons of 36% alcohol.

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29% and 57%
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