You are running a concession stand at a basketball game. You are selling pizza slices and sodas. Each pizza slice sells for $2.50 and each soda sells for $1.25. At the end of the night you made a total of $696.25. You sold a total of 384 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?
Responses
P + S = 696.25 and P + S = 384
2.50P + 1.25S = 696.25 and P + S = 384
2.50 + 1.25 = 696.25 and P + S = 384
2.50S + 1.25P = 384 and P + S = 696.25
2.50P + 1.25S = 696.25 and P + S = 384
The correct equations to solve this problem are:
2.50P + 1.25S = 696.25 and P + S = 384
The correct equation to solve this problem is:
2.50P + 1.25S = 696.25
In this equation, P represents the number of pizza slices sold and S represents the number of sodas sold.
To explain how to arrive at this equation, we need to consider the two pieces of information given in the problem:
1. The total amount of money made is $696.25
2. The total number of pizza slices and sodas sold combined is 384
Since each pizza slice sells for $2.50 and each soda sells for $1.25, we can express the total amount of money made in terms of the number of pizza slices and sodas sold.
The total revenue from pizza slices is 2.50P (2.50 multiplied by the number of pizza slices sold), while the total revenue from sodas is 1.25S (1.25 multiplied by the number of sodas sold).
Therefore, the equation 2.50P + 1.25S = 696.25 represents the total revenue made from selling pizza slices and sodas.
Additionally, we know that the total number of pizza slices and sodas sold combined is 384. This information can be represented by the equation P + S = 384.
Hence, the equation 2.50P + 1.25S = 696.25 and P + S = 384 are used to solve the problem.