Define your variables, write a system of equations, use your calculator to solve the system of equations and answer the problem.
A grocer sells milk chocolate at $2.90 per pound, dark chocolate at $4.40 per pound, and dark chocolate with almonds at $5.50 per pound. He wants to make a mixture of 50 pounds of mixed chocolates to sell at $4.65 per pound. The mixture is to contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined. How many pounds of each type must he use in this mixture?
Let's define our variables:
Let x = pounds of milk chocolate
Let y = pounds of dark chocolate
Let z = pounds of dark chocolate with almonds
Now let's write the system of equations based on the given information:
Equation 1: The cost of the mixture should be $4.65 per pound.
(2.90x + 4.40y + 5.50z) / 50 = 4.65
Equation 2: The mixture should contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined.
z = x + y
Now, let's use a calculator to solve this system of equations:
Solving Equation 2 for x, we have x = z - y.
Substituting the value of x in Equation 1, we get (2.90(z - y) + 4.40y + 5.50z) / 50 = 4.65.
Simplifying further: 2.90z - 2.90y + 4.40y + 5.50z = 4.65 * 50.
Combining like terms: 8.40z + 1.50y = 232.5.
Since we have two variables but only one equation, it is not possible to solve the system of equations to find unique values for x, y, and z.
So, unfortunately, we cannot determine how many pounds of each type the grocer must use in this mixture using this information.
Let's define our variables:
Let x represent the number of pounds of milk chocolate
Let y represent the number of pounds of dark chocolate
Let z represent the number of pounds of dark chocolate with almonds
We will write a system of equations to represent the given information:
Equation 1: x + y + z = 50 (The total weight of the mixture is 50 pounds)
Equation 2: (4.4y + 5.5z) = 2.9x (The total price of the mixture is equal to the price of the milk chocolate)
To solve this system of equations, we can use a calculator to find the values of x, y, and z.
Now let's use the calculator to solve the system of equations.
To solve this problem, let's define some variables:
Let x be the number of pounds of milk chocolate.
Let y be the number of pounds of dark chocolate.
Let z be the number of pounds of dark chocolate with almonds.
We can write a system of equations based on the information provided:
1. The price equation: 2.9x + 4.4y + 5.5z = 4.65(50) = 232.5
This equation represents the total cost of the mixture, which should be equal to the desired overall price ($4.65 per pound) multiplied by the total weight (50 pounds).
2. The quantity equation: x + y + z = 50
This equation represents the constraint that the total weight of the mixture should be 50 pounds.
3. The mixture equation: z = x + y
This equation represents the condition that the amount of dark chocolate with almonds should be equal to the sum of the milk chocolate and dark chocolate amounts.
To solve this system of equations using a calculator, follow these steps:
Step 1: Enter the coefficients of the variables and the constant terms into the matrix. For the price equation, we get:
[2.9 4.4 5.5 | 232.5]
For the quantity equation, we get:
[1 1 1 | 50]
For the mixture equation, we get:
[-1 0 1 | 0]
Step 2: Use the calculator's matrix functions to solve the system of equations. Different calculators have different procedures, but many have a built-in function to solve systems of linear equations.
Step 3: Once you have solved the system, the calculator will provide the values of x, y, and z. These values will represent the number of pounds of each type of chocolate that the grocer should use in the mixture.
Step 4: Use the obtained values to answer the problem.
That's not stats. You really ougth to avoid trying to help, you just don't know what you are doing.
Value:
50*4.65=2.90x+4.40y+5.50z
Weight:
50=x+y+z
Mix:
z=x+y
putting this in matrix form:
2.90x+4.40y+5.50z =4.65*50
x+ y + z= 50
x+y-z=0
you can solve this in any way you wish.
Here, with a matrix calculator
2.90, 4.40, 5.50, 232.5
1,1,1,50
1,1,-1,0
Answer:
x_1=10.00
x_2=15.00
x_3=25.00
https://matrixcalc.org/en/slu.html#solve-using-Gaussian-elimination%28%7B%7B29%2F10,22%2F5,11%2F2,0,465%2F2%7D,%7B1,1,-1,0,0%7D,%7B1,1,1,0,50%7D%7D%29
In order to solve this you must first give variables to each of the types of chocolate.
x = Milk chocolate
y = Dark chocolate
z = Dark chocolate with almonds
Now you can create two equations which you can use to solve for each of the variables.
50*4.65=2.90x+4.40y+5.50z
z=x+y
Now that you have these two equations, you can use substitution to solve for the variables.