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At a sporting event, the price for 3 cheeseburgers and 2 cups of lemonade is $14 and the price for 2 cheeseburgers and 4 cups of lemonade is $12. How much does it cost for 1 cheeseburger and 2 cups of lemonade?

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c= the price of a cheeseburger and l = the price of a lemonade:

[tex]3c + 2l=14\\2c+4l=12[/tex]

Divide the second equation by -2 to begin the process of solving by elimination:

[tex]3c + 2l=14\\-1/2\ (2c+4l=12)\\\\3c+2l=14\\-c-2l=-6\\\\2c=8\\c=4[/tex]

Now that we have c, 4, we can plug it in to one of the equations to find l:

[tex]3c + 2l=14\\3(4)+2l=14\\12+2l=14\\2l=2\\l=1[/tex]

So, each cheeseburger is $4 and each lemonade is $1.  The final answer is:

1 cheeseburger and 2 cups of lemonade would cost $6.
14 dollars= 3 cheeseburger plus 2 cups of lemonade
14=3[4]+2[1]=14
1 cheeseburger= 4 dollars
1 lemonade= 1 dollars
12 dollars= 2cheeseburger plus 4 cups of lemonade

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