Question 937413
You omitted a piece of information, but try this:
g = how many kilograms of juice B is in the mixture.


Amount of mixture is {{{g+10}}}  kilograms.



Look at the concentrations of apple and grape juice in the two different juice types:


Juice A:
(2/3) apple
(1/3) grape


Juice B:
(1/3) apple
(2/3) grape


Let a be how much juice A is in the mixture;
Let b be how much juice B is in the mix.



Again, your description did not show how much kilograms grape juice
was in the mix, so call this quantity, g.



Account for mass of apple juice.
{{{highlight_green((2/3)a+(1/3)b=10)}}}


Account for mass of grape juice.
{{{highlight_green((1/3)a+(2/3)b=g)}}}



Those are two linear equations in maybe three unknown variables, but one would
expect that you were given a clear value for "g" but simply forgot to show it
when you gave your problem description.


Simplify the two equation, and then solve the system of those two simultaneous equations.