SOLUTION: a lab needs to make 100 gallons of an 18% acis solution by mixing a 12% acid solition with a 20% solution. how many gallons of each solution are needed? word problems have neve

Question 27003: a lab needs to make 100 gallons of an 18% acis solution by mixing a 12% acid solition with a 20% solution. how many gallons of each solution are needed?
word problems have never been easy for me. i have always had trouble with them and this one has been really tough for me to figure out. ive been working on this problem for over 20 minutes and ive gotten everyone in my family to help me. and no one could figure it out. please help me or give me a clue on how do to this word problem. i have no idea. thank you very much.
Darcy
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
There's a little trick that is the key. Once you get it, it's hard to forget.
If I've got 100 gallons total, and it's divided into two parts, then
I can call those two parts S and (100 - S) where S is an unknown.
The rest is easy.
You've got a 12% solution and a 20% solution to start with
Ask yourself how much alcohol are in those solutions?
(12%)*(S) + (20%)*(100 - S)
What do you want that much alcohol to equal?
You want it to equal (18%)*(100), the final concentration
(12%)*(S) + (20%)*(100 - S) = (18%)*(100)

check
.12*25 + .2(100 - 25) = 18
3 + 15 = 18
It checks

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