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?"

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

Answer 2

To determine how many pounds of each ingredient the store used, we can set up a system of equations. Let's represent the pounds of gummy candy, jelly beans, and hard candy as g, j, and h, respectively.

From the information given, we know that the store makes an 8-pound mixture, so we have the equation:

g + j + h = 8

We also know that 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 total cost of the mixture is $20.00, so we have the equation:

2g + 3j + 3h = 20

Additionally, the mixture calls for four times as many gummy candy pieces as jelly beans, so we have the equation:

g = 4j

Thus, the system of equations that could be used to answer the question is:

g + j + h = 8
2g + 3j + 3h = 20
g = 4j

Answer 3

To determine the system of equations that can be used to answer the question, we need to consider the given information.

Let's assign variables to the unknowns in the problem:
- Let g be the weight of gummy candy in pounds.
- Let j be the weight of jelly beans in pounds.
- Let h be the weight of hard candy in pounds.

From the problem statement, we know the following information:
1) The candy store makes an 8-pound mixture. Therefore, the sum of the weights of the three ingredients g, j, and h is 8 pounds: g + j + h = 8.

2) The cost of the gummy candy is $2.00 per pound, the jelly beans cost $3.00 per pound, and the hard candy costs $3.00 per pound. Since the total cost of the mixture is given as $20.00, we can set up an equation for the cost:

2(g) + 3(j) + 3(h) = 20.

3) The mixture requires four times as many gummy candy pieces as jelly beans. This can be expressed as:

g = 4(j).

Therefore, the system of equations that can 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.