Let's assume that the weight of gummy candy (g) is x pounds.
According to the given information, the weight of jelly beans (j) would be x/4 pounds.
Since the total weight of the mixture is 8 pounds, we can create the equation:
x + x/4 + h = 8
Multiplying the equation by 4 to get rid of the fraction:
4x + x + 4h = 32
Combining like terms:
5x + 4h = 32
We also know that the cost of gummy candy (2x), jelly beans (3(x/4)), and hard candy (3h) adds up to $20.00.
So we can create a second equation:
2x + 3(x/4) + 3h = 20
Multiplying the equation by 4 to get rid of the fraction:
8x + 3x + 12h = 80
Combining like terms:
11x + 12h = 80
Now we have a system of equations:
5x + 4h = 32
11x + 12h = 80
To solve this system, we can use the method of substitution.
From the first equation:
4h = 32 - 5x
Dividing by 4:
h = (32 - 5x)/4
Substituting this value of h into the second equation:
11x + 12((32 - 5x)/4) = 80
Multiplying by 4 to get rid of the fraction:
44x + 12(32 - 5x) = 320
Expanding the expression:
44x + 384 - 60x = 320
Combining like terms:
-16x = -64
Dividing by -16:
x = 4
Substituting this value of x back into the first equation:
5(4) + 4h = 32
20 + 4h = 32
4h = 12
h = 3
Therefore, the candy store used 4 pounds of gummy candy, 1 pound of jelly beans, and 3 pounds of hard candy in the mixture.
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.
"How many lbs of each ingredient did the store use?"
1 answer
1 answer