You are running a concession stand at a baseball game. 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?

Answer 1

To solve for the number of pizza slices (P) and sodas (S) sold, we can set up a system of equations based on the information provided.

1. Equation for total sales: The total revenue from selling pizza slices and sodas is given by: \[ 3.50P + 1.50S = 800 \] This equation reflects the fact that each pizza slice sells for $3.50 and each soda sells for $1.50, totaling $800 in sales.

2. Equation for total items sold: The total number of items sold (both pizza slices and sodas) is: \[ P + S = 344 \] This equation indicates that the total number of pizza slices and sodas sold is 344.

Now you have the following system of equations:

1. \( 3.50P + 1.50S = 800 \)
2. \( P + S = 344 \)

You can solve this system using substitution or elimination. Here's how you might solve it using substitution:

1. Solve the second equation for S: \[ S = 344 - P \]

2. Substitute \( S \) in the first equation: \[ 3.50P + 1.50(344 - P) = 800 \]

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

4. Combine like terms: \[ (3.50 - 1.50)P + 516 = 800 \] \[ 2.00P + 516 = 800 \]

5. Subtract 516 from both sides: \[ 2.00P = 284 \]

6. Divide by 2.00 to solve for P: \[ P = 142 \]

7. Substitute P back into the equation for S: \[ S = 344 - P = 344 - 142 = 202 \]

So, the final results are:

• Number of pizza slices sold (P): 142
• Number of sodas sold (S): 202

In summary, the equations used are:

1. \( 3.50P + 1.50S = 800 \)
2. \( P + S = 344 \)