# Pre-cal

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?

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1. 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.

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2. 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
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

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bobpursley

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