Question

Assign two variables for each problem, and write the equations. Do not solve.

Answer 1

Call the amount of pineapple "P', and the amount of gingerale "G".

We know that a mix of pineapple and gingerale makes 200 cups. So: 
$P+G=200$

We also know that double the pineapple (i.e. 2P) and triple the gingerale (i.e. 3G) makes 420 cups. So:
$2P+3G=420$

We can now solve by substitution:
$2P+3(200-P)=420$
$2P+600-3P=420$
$-P=-180$
$P=180$

$180+G=200$
$G=20$

For 420 cups we need 2P=360 cups of pineapple and 3G=60 cups of gingerale]