Final answer:
The correct equation that models the relationship between the number of soccer tickets bought (x) and the total amount paid is y = 14x + 20, which is derived from solving two equations based on given scenarios about Mrs. Avila's and Mrs. Barrera's families' ticket purchases.
Step-by-step explanation:
The question asks us to find the equation that models the relationship between the number of soccer tickets bought (x) and the total amount paid. We are given two scenarios: Mrs. Avila's family pays $132 for 8 tickets plus parking, and Mrs. Barrera's family pays $90 for 5 tickets plus parking. We can use these scenarios to create two equations to solve for the price per ticket and the parking cost.
Let's assume that the price per ticket is p and the parking fee is a fixed cost c. For Mrs. Avila's family: 8p + c = $132. For Mrs. Barrera's family: 5p + c = $90. Subtracting the second equation from the first, we get: 3p = $42, which means p = $14. Plugging this value back into one of the original equations to solve for c, we get: c = $132 - 8(14), which simplifies to c = $20. Therefore, the equation modeling the relationship is y = 14x + 20, which is option D.