Let's call the amount of gummy candy g pounds, the amount of jelly beans j pounds, and the amount of hard candy h pounds.
The first equation we can write is the total weight of the mixture:
g + j + h = 8
The second equation we can write is the equation for the cost of the mixture:
2g + 3j + 3h = 20
We also know that the mixture calls for four times as many gummy candy pieces as jelly beans, so we can write the third equation:
g = 4j
So the system of equations that could be used to answer the question "How many lbs of each ingredient did the store use?" is:
g + j + h = 8
2g + 3j + 3h = 20
g = 4j