Question 652559: A 20% solution of fertilizer is to be mixed with a 80% solution of fertilizer in order to get 120 gallons of a 60% solution. How many gallons of the 20% solution and 80% solution should be mixed?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Let the number of gallons of 20% solution of fertilizer to be used be  .
Let the number of gallons of 80% solution of fertilizer to be used be  .
As you mix the solutions, the volumes add up,
so the final volume (in gallons) is  .
That is your first equation.
gallons of a 20% solution contain  gallons of fertilizer.
gallons of a 80% solution contain  gallons of fertilizer.
When you mix them, the final mix will contain  gallons of fertilizer,
but that must be the amount of fertilizer in 120 gallons of 60% solution of fertilizer,
which is  gallons of fertilizer.
So  or  (which means the same in math class).
That is your second equation.
You now have a system of 2 equations linear in two variables:
You can solve it by whatever method you chose.
For example, to solve by elimination, you may chose to multiply the first equation by  , getting
 ,
and add it to the second equation, getting
 -->  --> 
Now, from  and , you get
 -->  --> 
NOTES FROM A CHEMIST
In real life, volume is often additive, so if you mix gallons of a solution with gallons of another solution, you get  gallons of mixture. (In math problems, volume is always additive).Chemists (like me) specify very clearly the concentration of a solution.
If we say 20% weight in weight (w/w), we mean that 100 g of solution contains 20 g of the item of interest.
If we say 20% weight in volume (w/v), we mean that 100 milliliters of solution contains 20 g of the item of interest.
If we say 20% volume in volume (v/v), we mean that 100 gallons of solution contains 20 gallons of a liquid of interest.
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