Answer: the cost of one Soda was $1.75
Explanation:
Let x represent the cost of one hot dog.
Let y represent the cost of one Soda.
At the baseball game, Adam bought 3 hot dogs and 2 sodas for $11. It means that
3x + 2y = 11 - - - - - - - - - - 1
In a later time, he purchased 2 hot dogs and 3 sodas for $10.25. It means that
2x + 3y = 10.25 - - - - - - - - -2
Multiplying equation 1 by 2 and equation 2 by 3, it becomes
6x + 4y = 22
6x + 9y = 30.75
Subtracting, it becomes
- 5y = - 8.75
y = - 8.75/- 5
y = 1.75
Substituting y = 1.75 into equation 1, it becomes
3x + 2 × 1.75 = 11
3x + 3.5 = 11
3x = 11 - 3.5 = 7.5
x = 7.5/3 = 2.5