Question 151324
a)

Let x=# of pepperoni sold, y=# of sausage sold, and z=# of cheese sold 



b)

Since there are 3 unknowns, we need 3 equations:


Equation #1:

First, since they sold "pepperoni for $12, sausage for $10, and cheese for $8" and collected $5,900, this means that {{{12x+10y+8z=5900}}}


Equation #2:

Also, we know that the students sold 600 pizzas total. So this means that the sum of all of the pizzas sold was 600. So this translates to {{{x+y+z=600}}}. 



Equation #3:

Finally, since they sold "175 more cheese pizzas than sausage pizzas", this makes the equation {{{z=y+175}}}



Getting all of the variables to one side for equation 3 gives us: {{{0x-y+z=175}}}



So we have the system 



{{{system(12x+10y+8z=5900,x+y+z=600,0x-y+z=175)}}}



c)


This means that we have the augmented matrix matrix


{{{(matrix(3,4,12,10,8,5900,1,1,1,600,0,-1,1,175))}}}



d)


Solution was generated by the <a href="http://www.math.odu.edu/~bogacki/lat/">Linear Algebra Toolkit</a>


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/augmentedmatrix.png" alt="Photobucket - Video and Image Hosting">



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Answer:



So the solutions are {{{x=225}}}, {{{y=100}}}, and {{{z=275}}} (these values form the right hand column of the augmented matrix).




So this means that they sold 225 pepperoni pizzas, 100 sausage pizzas, and 275 cheese pizzas.