John is making punch. how many cups of 50% juice should he add to a drink that contains 10% juice if he wants to make 15 cups of punch containing 20% juice? (how many cups of each drink)

define one variable based on the percentage of which is being asked.

set up table (which wants the percent and amt of mixture a and mixture b)

solve for x.

Lets make a equal the amount of mixture a and b the amount of mixture b.  You can made an equation .10a+.50b=.20(15) and a+b=15.  So then you make the system of equations:
.10a+.50b=3
a+b=15
I would substitute b in the first equation with b=15-a to get the single equation .10a+.50(15-b)=3 and then solve for b.
.10a+7.5-.5a=3
-.4a+7.5=3
-.40b=-4.5
a=11.25
With that value of a you can find that b=3.75
Therefore you you have to mix 11.25 cups of 10% juice with 3.75 cups of 50% juice to get 15 cups of 20% juice.

This is how I would solve the question.  I don't really know what the question means by setting up a table so I hope this method is fine. If it is not please let me know in the comments so that I can try to fix it.
I hope this helps.

P.S. Let me know if you want me to try to explain to you how I got my first equation.  You have to use knowledge that you will eventually learn in chemistry when going over the unit that introduces you to solutions.