SOLUTION: Fruit just A is composed of 2 parts apple juice and 1 part grape juice. Fruit juice B is composed of 1 part apple juice and 2 part grape juice. When A and B are mixed, the new mixt

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Question 937413: Fruit just A is composed of 2 parts apple juice and 1 part grape juice. Fruit juice B is composed of 1 part apple juice and 2 part grape juice. When A and B are mixed, the new mixture has 10kg of apple juice and kg of grape juice. How many kilograms does each type of original fruit juice weigh? Ans.{A:____
Ans.{B:____
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B10 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%28%282%2F3%29a%2B%281%2F3%29b=10%29

Account for mass of grape juice.
highlight_green%28%281%2F3%29a%2B%282%2F3%29b=g%29


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.