Final answer:
To find the number of toppings at which the pizzas cost the same, we can set the total cost expressions for both pizzas equal to each other and solve for 'x'. After 4 additional toppings, the pizzas will cost the same. With 5 additional toppings, Johnson's Pizza costs more.
Step-by-step explanation:
To find the point at which the pizzas cost the same, we need to determine the number of toppings that will make the total cost equal for both pizzas. Let's denote the number of additional toppings as 'x', and the cost of each additional topping at Fine Dough Pizza as $1.50, and at Johnson's Pizza as $2.00. The total cost for Fine Dough Pizza will be $10.00 + $1.50x, and the total cost for Johnson's Pizza will be $8.00 + $2.00x. To find the number of toppings at which the pizzas cost the same, we can set the two total cost expressions equal to each other and solve for 'x':
$10.00 + $1.50x = $8.00 + $2.00x
To solve the equation, we can subtract $1.50x from both sides:
$10.00 = $8.00 + $0.50x
Next, we subtract $8.00 from both sides:
$2.00 = $0.50x
To isolate 'x', we divide both sides by $0.50:
x = 4
Therefore, after 4 additional toppings, the pizzas will cost the same.
To determine which pizza costs more with additional toppings, we can compare the total cost expressions for both pizzas for a specific number of toppings. For example, let's consider 5 additional toppings:
Total cost at Fine Dough Pizza = $10.00 + $1.50(5) = $10.00 + $7.50 = $17.50
Total cost at Johnson's Pizza = $8.00 + $2.00(5) = $8.00 + $10.00 = $18.00
Therefore, with 5 additional toppings, Johnson's Pizza costs more.