Final answer:
Patman Pizza and Simple Simon's Pizza have different pricing functions, and by graphing these functions, the break-even point is found at six large pizzas. Below six pizzas, Patman Pizza is cheaper; above six, Simple Simon's is the better option.
Step-by-step explanation:
To determine which pizza place has the better deal for a certain number of large pizzas, we need to write a linear function for each place. For Patman Pizza, the cost C of ordering p large pizzas is C = 4 + 9p. For Simple Simon's Pizza, the function is C = 10 + 8p. Graphing both equations on the same coordinate plane, we can find the break-even point, where the costs are equal.
The break-even number of pizzas is found by setting the two cost equations equal to each other: 4 + 9p = 10 + 8p. Solving for p gives us p = 6. Therefore, for six pizzas, the cost from both companies is the same. For fewer than six pizzas, Patman Pizza is cheaper, and for more than six, Simple Simon's Pizza is cheaper.
Which company I would use depends on the number of pizzas I am planning to order. If it's less than six, I would choose Patman Pizza, otherwise, I would opt for Simple Simon's Pizza.