Question

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

The Math Club is having their end-of-the-year party. Natasha found that the cafeteria usually makes 200 cups of pineapple-ginger ale fruit punch. The cook told her that if she doubles the pineapple and triples the ginger ale, she will have a total of 420 cups of punch. How many cups of each are needed to make 420 cups of fruit punch?

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]