A grocer wants to m,ix three kinds of hard candy to sell for $2.40 per pound. He need 50 pounds of candy altogether. He mixes sour balls worth $3.50 per pound,butterballs worth $2.50 per pound, and starlight mints worth $1.75 per pound. He mixes twice as many butterball as sour balls. Write a system of equations to find the number of pounds of each kind of candy he mixes together
We learned how to do matrices and we need to use them for this problem but i don't know how to set it up
_______ X _______
something X something?
To set up a system of equations using matrices, we need to define the variables and the given information. Let's denote the number of pounds of sour balls as 'x', the number of pounds of butterballs as 'y', and the number of pounds of starlight mints as 'z'.
We have three variables, so we will have three equations based on the given information. Let's write down the equations step by step:
1. The grocer needs 50 pounds of candy altogether:
x + y + z = 50
2. The grocer needs to mix twice as many butterballs as sour balls:
y = 2x
3. The grocer wants the candy to sell for $2.40 per pound. To find the equation for the cost per pound, we can multiply the number of pounds of each type of candy by its respective price and sum them up, then divide by the total number of pounds:
(3.50x + 2.50y + 1.75z) / 50 = 2.40
Now that we have our three equations, we can represent them using a matrix equation. The matrix equation will have a coefficient matrix, variable matrix, and a constant matrix.
Let's set up the matrices:
Coefficient matrix:
[1 1 1]
[0 -2 0]
[3.50 2.50 1.75]
Variable matrix:
[x]
[y]
[z]
Constant matrix:
[50]
[0]
[2.40 * 50]
Now, we can represent the system of equations as a matrix equation:
Coefficient matrix * Variable matrix = Constant matrix
[1 1 1] [x] [50]
[0 -2 0] * [y] = [0]
[3.50 2.50 1.75] [z] [120]
This matrix equation represents the system of equations, and you can proceed to solve it using matrix operations or other methods to find the values of 'x', 'y', and 'z'.