Final answer:
The price of a soda is determined to be $150.00 by setting up a system of equations from the given purchases, solving for the cost of a cookie first and then finding the cost of a soda.
Step-by-step explanation:
To find the price of a soda, we need to set up a system of equations based on the information provided:
- Maggie bought three cookies and a soda for $300.00
- Elsa bought two cookies and two sodas for $400.00
Let's denote the cost of a cookie as 'c' and the cost of a soda as 's'.
From Maggie's purchase, we get the equation 3c + s = 300. (1)
From Elsa's purchase, we get the equation 2c + 2s = 400. (2)
To solve for 's', we can multiply equation (1) by 2 to eliminate 'c' when subtracted from equation (2). This gives us:
- 6c + 2s = 600 (3)
- 2c + 2s = 400 (2)
Subtracting equation (2) from equation (3) gives us:
Substituting 'c = 50' into equation (1) gives us:
- 3(50) + s = 300
- 150 + s = 300
- s = 150
Therefore, the price of a soda is $150.00.