Solve the following word problem using any method. show your work.
courtney finds a company willing to send her meals-ready-to-eat (mres) at a discounted price. cases of small portion meals are $20.00 each and cases of large portion meals are $30.00 each. she buys a total of 20 cases and spends a total of $450.00. how many of each case did she purchase?
courtney purchased cases of small portion meals
and cases of large portion meals.

Let's set up two equations:
x+y=20             We know she brought total of 20, some of each so x=small y=big
20x+ 30y=450
 
 x+y= 20
   -y    -y
 
 x= 20 -y

substitute into the other equation:    
20 (20-y) + 30y = 450
400 - 20y + 30y = 450
400+ 10 y = 450
10 y = 50
y= 5

So she brought  5 big cases.  Then substitute the value of y into one of the equations.

5+ x = 20 
x= 15

So we bought 15 small cases and 5 big cases. 

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Courtney purchased 15 cases of small portion meals and 5 cases of large portion meals.

The equation is y=17(7)+600 and it equals 717