SOLUTION: How much of Brand A fruit punch (45 % fruit juice) must be mixed with 2 gal. of Brand B fruit punch (35% fruit juice) to create a mixture containing 43% fruit juice?

Question 710335: How much of Brand A fruit punch (45 % fruit juice) must be mixed with 2 gal. of Brand B fruit punch (35% fruit juice) to create a mixture containing 43% fruit juice?
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Let's analyze the problem and put everything into variables.
Low concentration L=35%
High concentration H=45%
Target fruit juice concentration T=43%
Amount of low juice conc. punch u= 2 gallons
Amount of high conc. punch v = unknown
Amount of punch mixture M = also unknown

Note that u+v=M. Using this in the concentration's rational equation will be best this way.

We need this equation:

Our variable to solve for is v.

uL+vH=T(u+v)
uL+vH=Tu+Tv
vH-Tv+uL=Tu
vH-vT=uT-uL
.

Now, just substitute the given values into that formula for v and compute. That will be the volume in gallons of Brand A to add to the 2 gallons of Brand B punch. Be aware in practice you might want to know 128 fluid ounces per gallon.
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