Final answer:
To find the cost for 15 friends to buy tickets, we can create a linear equation using the costs for 4 and 6 tickets. The total cost equation is y = 8x + 2.95, where x is the number of tickets. Using this equation, the cost for 15 tickets is $122.95.
Step-by-step explanation:
To determine the cost for a group of 15 friends to buy tickets for the high school football game, we can use the information given for 4 and 6 tickets to create a linear equation. Let x represent the number of tickets, and y represent the total cost. From the problem, we know that:
- For 4 tickets, the cost is $34.95.
- For 6 tickets, the cost is $50.95.
We can express these as two points on the cost function: (4, 34.95) and (6, 50.95). To find the equation of the line, we first calculate the slope (m) of the line.
Slope (m) = (change in cost) / (change in tickets)
m = (50.95 - 34.95) / (6 - 4) = 16 / 2 = 8
Therefore, the cost per ticket is $8. To find the initial processing fee, we can plug one of the points into the line equation y = mx + b, where b is the processing fee. Using the point (4, 34.95):
34.95 = 8(4) + b
34.95 = 32 + b
b = 34.95 - 32 = 2.95
The total cost equation is y = 8x + 2.95. Using this equation, we can calculate the cost for 15 tickets:
y = 8(15) + 2.95
y = 120 + 2.95
y = 122.95
Therefore, the cost for 15 tickets will be $122.95.