Question

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Answer 1

Ok so we have
1 cup of mix=2 cups of water
you can make one of 2 assumptions
1. the mix disolves in the water and doesn't take up space (if so go to AAAAAAAAAAAA)

2. the mix doesn't disolve and takes up space (if so go to BBBBBBBBB)


AAAAAAAAAAA
so since the mix doesn't take up space, the pitcher volume=water volume
pitcher volume=20
water volume=20

mix=1/2 of water volume
mix=1/2 of 20
mix=1/2 times 20
mix=10 cups


BBBBBBBBBBBBBB
if the mix does take space
1:2
we add them
1+2=3
3 cups is 1 unit of mix and water
how many 3's are in 20

20/3=6 and 2/3 cups

so
mix=1 unit=6 and 2/3 cups
water=2 unit=2 times 6 and 2/3=13 and 1/3

water=13 and 1/3 cup
mix=6 and 2/3 cup




depends on which assumption you make


if AAAAAAAA
mix=10 cups

if BBBBBBBBB
water=13 and 1/3 cup
mix=6 and 2/3 cup

Answer 2

Ok, First put all the information into an equation. You have 20 gallons of water. You need 2 gallons for every 1 cup of energy drink mix. 
It should look like this:
c=cups of energy drink mix
c=20/2 
We are finding the number of cups (c) so we need to take the full amount of water (20 gallons) and dividing it by 2 because For every 1 cup, we need 2 Cups of drink mix. 
Simply:
c=20/2       =        c=10
you will need 10 cups of drink mixed to make 20 gallons of energy drink. 
Answer:
10 cups.