SOLUTION: You wish to mix wine with 25% alcohol and peach schnapps with 50% alcohol to obtain a different drink. How many liters of wine would you need to make 20 liters of the mixture with

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Question 186933: You wish to mix wine with 25% alcohol and peach schnapps with 50% alcohol to obtain a different drink. How many liters of wine would you need to make 20 liters of the mixture with a 40% alcohol content?
Could you help me set up the table to solve this I'm completely lost and I don't know where to put what in the table and what to do with it afterword.
Answer by ptaylor(1894) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, YOU DO THE TABLE AND I WILL SET UP THE EQUATION :
Let x= amount of wine needed
Then 20-x=amount of peach schnapps needed
Amount of pure alcohol before the mixture = amount of pure alcohol after they are mixed, so:
0.25x + 0.50(20-x)=0.40*20 get rid of parens
0.25x+10-0.50x=8 subtract 10 from each side
0.25x+10-10-0.50x=8-10 collect like terms
-0.25x=-2 divide each side by -0.25
x=8 liters-----------amount of wine needed
CK
8*0.25+0.50*12=0.40*20
2+6=8
8=8
Now you could solve this problem using two unknowns:
Let x=amount of wine
y=amount of schnapps
x+y=20------------------------eq1
0.25x+0.50y=0.40*20 or
0.25x+0.50y=8--------------------eq2
Hope this helps----ptaylor