Come up with a real-life situation and show how it might be modeled algebraically with a system of equations (or inequalities). Be sure to include:

A few sentences explaining the situation.

Your variables of choice and what each represents.

How you would set up and solve algebraically.

You are running a concession stand at a tennis game. You are selling hot dog and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night, you made a total of $78.50. You sold a total of 87 hot dog and sodas combined. You must report the number of hot dog sold and the number of sodas sold. How many hot dog was sold and how many sodas were sold? 1. Let's start by identifying the important information: hot dog cost $1.50Sodas cost $0.50Made a total of $78.50Sold 87 hot dog and sodas combined2. Define your variables. Ask yourself, "What am I trying to solve for? What don't I know? In this problem, I don't know how many hot dogs or sodas were sold. So this is what each variable will stand for. (Usually, the question at the end will give you this information). Let x = the number of hot dogs sold y = the number of sodas sold3. Write two equations. One equation will be related to the price and one equation will be related to the quantity (or number) of hot dogs and sodas sold. 1.50x + 0.50y = 78.50 (Equation related to cost) x + y = 87 (Equation related to the number sold) 4. Solve! We can choose any method that we like to solve the system of equations. I am going to choose the substitution method since I can easily solve the 2nd equation for y. 5. Think about what this solution means. x is the number of hot dogs and x = 35. That means that 35 hot dogs were sold. y is the number of sodas and y = 52. That means that 52 sodas were sold. 6. Write your answer in a complete sentence. 35 hot dogs were sold and 52 sodas were sold. 7. Check your work by substituting. 1.50x + 0.50y = 78.50 1.50 (35) + 0.50 (52) = 78.50 52.50 + 26 = 78.50 AND x + y = 87

35 + 52 = 87

Since both equations check properly, we know that our answers are correct!