You are running a concession stand at a baseball game.

Question

You are selling pizza slices and sodas.

Each pizza slice sells for $3.50 and each soda sells for $1.50.

At the end of the night, you made a total of $800.

You sold a total of 344 pizza slices and sodas combined.

You must report the number of pizza slices sold and the number of sodas sold.

What equations did you use to solve this, where P = the number of pizza slices sold and S = the number of sodas sold?

GPT-4o mini · Answer

To solve this problem, we can set up a system of equations based on the information provided.

Let:

We have two pieces of information that we can translate into equations:

Total number of items sold: The total number of pizza slices and sodas sold is 344. \[ P + S = 344 \]
Total revenue generated: The total sales from the pizza slices and sodas is $800. Since each pizza slice sells for $3.50 and each soda sells for $1.50, we can express this as: \[ 3.50P + 1.50S = 800 \]

Now we have the following system of equations:

To solve these equations, you can use substitution or elimination. Here, we will solve it using substitution.

From the first equation, solve for $ S $: \[ S = 344 - P \]

Now, substitute this expression for $ S $ into the second equation: \[ 3.50P + 1.50(344 - P) = 800 \]

Distribute the $ 1.50 $: \[ 3.50P + 516 - 1.50P = 800 \]

Combine like terms: \[ (3.50 - 1.50)P + 516 = 800 \] \[ 2P + 516 = 800 \]

Now, isolate $ P $: \[ 2P = 800 - 516 \] \[ 2P = 284 \] \[ P = 142 \]

Now that we have $ P $, substitute it back to find $ S $: \[ S = 344 - 142 \] \[ S = 202 \]

So, the number of pizza slices sold is $ P = 142 $ and the number of sodas sold is $ S = 202 $.

To summarize, the equations used were: