Question

A candy store makes an 8-pound mixture of gummy candy (g), jelly beans (j), and hard candy (h). The cost of gummy candy is $2.00 per pound, jelly beans cost $3.00 per pound, and hard candy costs $3.00 per pound. The mixture calls for four times as many gummy candy pieces as jelly beans. The total cost of the mixture is $20.00. Question 1 Which system of equations could be used to answer the question, "How many lbs of each ingredient did the store use?"

Answer 1

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