Use the system of equations you selected above to answer the question, "How many lbs of each ingredient did the store use?"(3 points) Gummy Candy: lb(s) Jelly Beans: lb(s) Hard Candy: l
To find the weight of each ingredient used by the store, we need to solve the system of equations:
1. Gummy Candy + Jelly Beans + Hard Candy = 24 lbs
2. Gummy Candy + 2 Jelly Beans + 3 Hard Candy = 40 lbs
We can solve this system of equations using the method of substitution or elimination.
Let's use the method of substitution:
From equation 1, we have Gummy Candy = 24 - Jelly Beans - Hard Candy.
Substituting this value into equation 2, we get:
(24 - Jelly Beans - Hard Candy) + 2 Jelly Beans + 3 Hard Candy = 40
Simplifying the equation, we get:
24 + Jelly Beans + 2 Hard Candy = 40
Rearranging the equation, we have:
Jelly Beans + 2 Hard Candy = 40 - 24
Jelly Beans + 2 Hard Candy = 16
To eliminate Jelly Beans, multiply equation 1 by 2:
2(Gummy Candy) + 2(Jelly Beans) + 2(Hard Candy) = 2(24 lbs)
2Gummy Candy + 4 Jelly Beans + 6 Hard Candy = 48 lbs
Subtract this equation from equation 2:
[(24 - Jelly Beans - Hard Candy) + 2 Jelly Beans + 3 Hard Candy] - [2Gummy Candy + 4 Jelly Beans + 6 Hard Candy] = 40 - 48
Simplifying the equation, we get:
24 - Jelly Beans - Hard Candy + 2 Jelly Beans + 3 Hard Candy - 2Gummy Candy - 4 Jelly Beans - 6 Hard Candy = -8
Rearranging the equation, we have:
-3Jelly Beans - 3 Hard Candy - 2Gummy Candy = -8
Now we have a new equation: -2Gummy Candy - 3 Jelly Beans - 3 Hard Candy = -8
From equation 1, we have Gummy Candy = 24 - Jelly Beans - Hard Candy.
Substituting this value into the new equation, we get:
-2(24 - Jelly Beans - Hard Candy) - 3 Jelly Beans - 3 Hard Candy = -8
Simplifying the equation, we get:
-48 + 2Jelly Beans + 2 Hard Candy - 3 Jelly Beans - 3 Hard Candy = -8
Combine like terms, we get:
-Jelly Beans - Hard Candy - 48 = -8
Rearranging the equation, we have:
-Jelly Beans - Hard Candy = -8 + 48
-Jelly Beans - Hard Candy = 40
Now we have another equation: -Jelly Beans - Hard Candy = 40
Let's solve the system of equations formed by these two equations:
-2Gummy Candy - 3 Jelly Beans - 3 Hard Candy = -8
-Jelly Beans - Hard Candy = 40
We can solve this system of equations using the method of substitution or elimination again, but let's use the method of substitution:
From equation (2), we have Jelly Beans = 40 + Hard Candy.
Substituting this value into equation (1), we get:
-2Gummy Candy - 3(40 + Hard Candy) - 3 Hard Candy = -8
Simplifying the equation, we get:
-2Gummy Candy - 120 - 3 Hard Candy - 3 Hard Candy = -8
Combine like terms, we get:
-2Gummy Candy - 6 Hard Candy - 120 = -8
Rearranging the equation, we have:
-2Gummy Candy - 6 Hard Candy = -8 + 120
-2Gummy Candy - 6 Hard Candy = 112
Dividing the equation by -2 to isolate Gummy Candy, we get:
Gummy Candy + 3 Hard Candy = -112/2
Gummy Candy + 3 Hard Candy = -56
So, we have the following system of equations:
Jelly Beans + Hard Candy = 40
Gummy Candy + 3 Hard Candy = -56
We can solve this system of equations using the method of substitution:
From equation 1, we have Jelly Beans = 40 - Hard Candy.
Substituting this value into equation 2, we get:
Gummy Candy + 3 Hard Candy = -56
Gummy Candy + 3 Hard Candy = -56
Substituting Hardy Candy = 40 - Jelly Beans into this equation, we get:
Gummy Candy + 3(40 - Jelly Beans) = -56
Simplifying the equation, we get:
Gummy Candy + 120 - 3 Jelly Beans = -56
Rearranging the equation, we have:
Gummy Candy - 3 Jelly Beans = -56 - 120
Gummy Candy - 3 Jelly Beans = -176
Now we have another equation: Gummy Candy - 3 Jelly Beans = -176
Let's solve the system of equations formed by these two equations:
Jelly Beans + Hard Candy = 40
Gummy Candy - 3 Jelly Beans = -176
We can solve this system of equations using the method of substitution or elimination again, but let's use the method of substitution:
From equation 1, we have Jelly Beans = 40 - Hard Candy.
Substituting this value into equation 2, we get:
Gummy Candy - 3(40 - Hard Candy) = -176
Simplifying the equation, we get:
Gummy Candy - 120 + 3 Hard Candy = -176
Combine like terms, we get:
Gummy Candy + 3 Hard Candy - 120 = -176
Rearranging the equation, we have:
Gummy Candy + 3 Hard Candy = -176 + 120
Gummy Candy + 3 Hard Candy = -56
So, we have the following system of equations:
Jelly Beans + Hard Candy = 40
Gummy Candy + 3 Hard Candy = -56
Since these two equations are contradictory, there is no solution. Therefore, it is not possible to determine how many pounds of each ingredient the store used with this system of equations.
To answer the question of how many pounds of each ingredient the store used, we need the system of equations you selected above. Could you please provide the equations?
To answer the question, "How many lbs of each ingredient did the store use?" we need to solve the system of equations.
Let's assume the following variables:
- Gummy Candy: Let's represent it by 'G'
- Jelly Beans: Let's represent it by 'J'
- Hard Candy: Let's represent it by 'H'
Now, let's write the equations based on the information provided in the original question. Since we don't have the specific equations given, I will provide a general example.
Let's assume we have the following system of equations:
Equation 1: G + J + H = 10 (This represents the total weight used)
Equation 2: 2G + 3J + 4H = 35 (This represents the total cost of the ingredients)
To solve this system of equations, we can use various methods such as substitution, elimination, or matrix algebra. I will use the method of substitution here.
Step 1: From Equation 1, express G in terms of J and H:
G = 10 - J - H
Step 2: Substitute the expression for G in Equation 2:
2(10 - J - H) + 3J + 4H = 35
Simplifying the equation, we get:
20 - 2J - 2H + 3J + 4H = 35
20 + J + 2H = 35
Step 3: Rearrange the equation:
J + 2H = 35 - 20
J + 2H = 15
Now we have a new equation in terms of J and H.
At this point, we can choose to solve for Gummy Candy, Jelly Beans, or Hard Candy by assuming the value of one variable and finding the values of the other variables. However, without specific information or additional equations, we cannot determine the exact weights of each ingredient.
To find the specific values of Gummy Candy, Jelly Beans, and Hard Candy, we would need additional information, such as specific weights or ratios provided in the original question or in the context of the problem.