Use your choice of equal values, substitution, or elimination to solve the following System of Equations, and show your work.
i are running a concession stand at a basketball game. You are selling hot
dogs and sodas. Each hot dog costs $3.00 and each soda costs $2.00. At the
end of the night you made a total of $213.00. You sold a total of 87 hot dogs
and sodas combined. You must report the number of hot dogs sold and the
number of sodas sold. How many hot dogs were sold and how many sodas
were sold?

For this scenario, I used the elimination method. Organize the equations, so it's easier to subtract from each other. My x-variable will represent the number of hot dogs and my y-variable will represent the number of sodas.

3x+2y=213

x  + y =87

We need to make sure one of the monomials are alike in each equation, so we can eliminate a variable. Distribute 3 to each number/variable in the second equation.

3x+2y=213

3(x+y=87) --> 3x+3y=261

Now we can eliminate x.

  3x+2y=213

-  3x+3y=261

        -y=-48  

Divide -1 to both sides to get y=48. So, you sold 48 cans of soda. Now, we can find the number of hot dogs by substituting 48 into the second equation to get x+48=87. Subtract 48 to both sides to result with x=39. So, you sold 39 hot dogs.

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