Question 710335
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:
{{{(uL+vH)/(u+v)=T}}}
Our variable to solve for is v.


uL+vH=T(u+v)
uL+vH=Tu+Tv
vH-Tv+uL=Tu
vH-vT=uT-uL
.
{{{highlight(v=u(T-L)/(H-T))}}}


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.