A candy store makes a 9-pound mixture of gummy candy, jelly beans, and hard candy. 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 two times as many gummy candy pieces as jelly beans. The total cost of the mixture is $23.00. How much of each ingredient did the store use?%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A3 lbs. gummy candy, 2 lbs. jelly beans, 4 lbs. hard candy%0D%0A3 lbs. gummy candy, 2 lbs. jelly beans, 4 lbs. hard candy%0D%0A%0D%0A4 lbs. gummy candy, 2 lbs. jelly beans, 3 lbs. hard candy%0D%0A4 lbs. gummy candy, 2 lbs. jelly beans, 3 lbs. hard candy%0D%0A%0D%0A4 lbs. gummy candy, 3 lbs. jelly beans, 2 lbs. hard candy%0D%0A4 lbs. gummy candy, 3 lbs. jelly beans, 2 lbs. hard candy%0D%0A%0D%0A2 lbs. gummy candy, 3 lbs. jelly beans, 4 lbs. hard candy%0D%0A2 lbs. gummy candy, 3 lbs. jelly beans, 4 lbs. hard candy

Answer 1

To solve this problem, let's denote the number of pounds of gummy candy as G, the number of pounds of jelly beans as J, and the number of pounds of hard candy as H.

We are given that the total weight of the mixture is 9 pounds:
G + J + H = 9 (equation 1)

We are also given that the cost of gummy candy is $2.00 per pound, the cost of jelly beans is $3.00 per pound, and the cost of hard candy is $3.00 per pound. The total cost of the mixture is $23.00:
2G + 3J + 3H = 23 (equation 2)

The mixture calls for two times as many gummy candy pieces as jelly beans:
G = 2J (equation 3)

We can solve this system of equations to determine the values of G, J, and H.

From equation 3, we can substitute G = 2J into equation 1 and simplify:
2J + J + H = 9
3J + H = 9 (equation 4)

Now we have a system of two equations with two variables (equations 2 and 4). We can solve this system using substitution or elimination method.

Let's solve it using the substitution method:

From equation 4, we can solve for H:
H = 9 - 3J

Substitute this value of H into equation 2:
2G + 3J + 3(9 - 3J) = 23
2G + 3J + 27 - 9J = 23
2G - 6J = -4
G - 3J = -2 (equation 5)

Now we have a system of two equations with two variables (equations 3 and 5).

Substituting G = 2J from equation 3 into equation 5:
2J - 3J = -2
-J = -2
J = 2

Substitute this value of J into equation 3 to solve for G:
G = 2J
G = 2(2)
G = 4

Now substitute the values of G and J into equation 4 to solve for H:
3J + H = 9
3(2) + H = 9
6 + H = 9
H = 9 - 6
H = 3

So, the solution is G = 4, J = 2, and H = 3.

Therefore, the candy store used 4 pounds of gummy candy, 2 pounds of jelly beans, and 3 pounds of hard candy.