Question

You're finally home from your exotic vacation and are craving for some yummy American food: Pizza! A pizza at Anthonys Pizzeria cost $6.80 plus $0.90 per topping. A pizza at Ninos Pizzeria costs $7.30 plus $0.65 per topping. How many toppings would you need to add to each pizza in order for the pizzas to cost the same amount? Solve By Graphing. You May Use Desmos. Mark The Points

Answer 1

Let's use the variable x to represent the number of toppings and y to represent the cost of a pizza.

For the first pizza, the cost is $6.80 plus $0.90 times the number of toppings, so we can write the following equation:

`y=6.8+0.9x`

For the second pizza, the cost is $7.30 plus $0.65 times the number of toppings, so we can write our second equation:

`y=7.3+0.65x`

In order to calculate the number of toppings for the same price on both pizzas, let's equate the values of y and solve for x:

`\begin{gathered} 6.8+0.9x=7.3+0.65x \\ 0.9x-0.65x=7.3-6.8 \\ 0.25x=0.5 \\ x=(0.5)/(0.25) \\ x=2 \end{gathered}`

To solve this system graphically, we need to graph both equations and find the intersection point, which is the solution of the system.

To graph a linear equation, we need two ordered pairs that are solutions to the equation.

For the equation y = 6.8 + 0.9x, let's use the ordered pairs (0, 6.8) and (1, 7.7).

For the equation y = 7.3 + 0.65x, let's use the ordered pairs (0, 7.3) and (1, 7.95):

Looking at the graph, the intersection point occurs at x = 2, therefore the number of toppings for the same prices is 2.