Final answer:
The correct system of equations representing the cost of hot dogs and candy is 4x + 7y = 14.37 and 12x + 9y = 25.75, where 'x' is the cost of a hot dog and 'y' is the cost of a bag of candy.
Step-by-step explanation:
To find out the cost of a hot dog, we need to solve a system of linear equations that represent the situation described. According to the question, four hot dogs and seven bags of candy cost $14.37. This can be represented by the equation 4x + 7y = 14.37, where 'x' is the cost of a hot dog and 'y' is the cost of a bag of candy. The second part of the question states that twelve hot dogs and nine bags of candy cost $25.75. This gives us the second equation, 12x + 9y = 25.75. Therefore, the correct system of equations is represented by option B.