SOLUTION: I am in desparate need of assistance with augmented matrix. I need to solve the following situation: A group of students decides to sell pizzas to help raise money for their seni

Question 141799: I am in desparate need of assistance with augmented matrix. I need to solve the following situation: A group of students decides to sell pizzas to help raise money for their senior class trip. They sold pepperoni for $12, sausage for $10, and cheese for $8. At the end of their sales the class sold a total of 600 pizzas and made $5900. The students sold 175 more cheese pizzas than sausage pizzas. Set up a system of three equations and three unknowns, use an augmented matrix to solve. Identify the three unknowns. Write a separate equation representing each of the first three sentences. Determine the augmented matrix that represents the three equations and solve for the matrix.
And finally,how many of each type of pizza were sold?
If any one can assistance I would appreciate the help.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A group of students decides to sell pizzas to help raise money for their senior class trip.
They sold pepperoni for $12, sausage for $10, and cheese for $8.
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At the end of their sales the class sold a total of 600 pizzas and made $5900.
Quantity Eq: p + s + c = 600
Value Eq: 12p + 10s + 8c = 5900
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The students sold 175 more cheese pizzas than sausage pizzas.
Relation Eq: c = s + 175
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Set up a system of three equations and three unknowns, use an augmented matrix to solve. Identify the three unknowns.
---------------------------
Write a separate equation representing each of the first three sentences.
p + s + c = 600
12p + 10s + 8c = 5900
0 - s + c = 175
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Comment: You can write these as an aumented matix
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Solve the system anyway you can to get:
p = 225 (# of pepperoni sold)
s = 100 (# of sausage sold)
c = 275 (# of cheese sold)
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Determine the augmented matrix that represents the three equations and solve for the matrix.
=====================
Cheers,
Stan H.

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