SOLUTION: My question is: Suppose that you have a supply of a 30%solution of alcohol and 70% of solution of alcohol. how many quartz of each should be mixed to poduce 20 quartz that is 40%a

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Question 154285: My question is: Suppose that you have a supply of a 30%solution of alcohol
and 70% of solution of alcohol. how many quartz of each should be mixed to poduce 20 quartz that is 40%alcohol?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of 30% solution needed
Then 20-x=amount of 70% solution needed
Now we know that the pure alcohol in the 30% solution (0.30x) plus the amount of pure alcohol in the 70% solution (0.70(20-x)) has to equal the amount of pure alcohol in the final mixture (0.40*20) so our equation to solve is:
0.30x+0.70(20-x)=0.40*20 get rid of parens
0.30x+14-0.70x=8 subtract 14 from each sidwe
0.30x+14-14-0.70x=8-14 collect like terms
-0.40x=-6 divide each side by -0.40
x=15 quarts----------------------------amount of 30% solution needed
20-x=20-15=5 quarts-----------------------amount of 70% solution needed
CK
15*0.30+5*0.70=20*0.40
4.5+3.5=8
8=8

Hope this helps---ptaylor