Short Answer 
The solution involves defining variables for the number of slices of pizza (x) and sodas (y), leading to two equations based on expenses. By solving these equations, it was determined that one slice of pizza costs $2.25 and one soda costs $1, resulting in a total cost of $5.25 for one slice and three sodas.
Step 1: Define Variables and Set Up Equations
To solve the problem, we first need to define our variables. Let x represent the number of slices of cheese pizza and y represent the number of sodas purchased. We will then create two equations based on Richard’s and Jordan’s total expenses:
- For Richard: $8.75 = 3x + 2y
- For Jordan: $8.50 = 2x + 4y
Step 2: Solve the Equations
Next, we will graph the equations obtained to find their intersection point. This point gives us the values of x (slices of pizza) and y (sodas). The intersection point is calculated to be (2.25, 1), which means:
- One slice of pizza costs $2.25
- One soda costs $1
Step 3: Calculate Total Cost
Now that we have the prices, we can find the total cost for one slice of pizza and three sodas. Using the found values, we substitute into the expression:
- Total cost, T = 1(2.25) + 3(1)
- Simplifying, we find T = 2.25 + 3 = $5.25
The final answer is $5.25.