SOLUTION: a pizzeria sells three sizes of pizza: small, medium, and large. the pizzas sell for $9, $10, and $13, respectively. one evening they sold 21 pizzas and received $220. if they sold

Question 1062362: a pizzeria sells three sizes of pizza: small, medium, and large. the pizzas sell for $9, $10, and $13, respectively. one evening they sold 21 pizzas and received $220. if they sold 1 more medium than large pizzas, how many of each size did they sell?
Use the Gaussian elimination method with back substitution to solve the given word problem
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
small=x
medium=y
large=z
x+y+z=21
9x+10y+13z=220
y=z+1
------------------
x+y+z=21
9x+10y+13z=220
y-z=1
----------------
first times -9 and add it to second
9x+10y+13z=220
-9x-9y-9z=-189
y-z=1
y+4z=31
y-z=1
--------------
multiply the third one by -1 and add to second
y+4z=31
-y+z=-1
5z=30
z=6
y=z+1
y=7
x+y+z=21, x=8
{8,7,6}
8*$9=$72
7*$10=$70
6*$13=$78
Total=21 and $220

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