## What's for Lunch? Pizza Cost Comparison

In this assignment you will visit the The Internet Pizza Server and compare costs for different combinations of toppings and pizza sizes. You will also have the opportunity to create and "order" a pizza of your choice.

 You may use a metric ruler to measure the size of the pizza on your screen, or you may check the image size (in pixels) by viewing the image online.   To do this, follow these steps (and see the example below): Right-click (use the right-hand or secondary mouse button) on the image and select "View Image" from the menu that will appear -- practice on the image at the right:

 To View an Image: Move your mouse pointer over the image and press the right mouse button. The pop-up menu should include a choice for "View Image" (see the example). Move your mouse to select (highlight) that line; then "click" with your left (primary) mouse button.
The image will appear by itself on the screen.

At the TOP of the screen the dimensions of the image will be listed as width by height (the mini-pizza in the example is 56 by 56 pixels).

After you make note of the size of the image, click the Back button to return to the previous page.

Go to the Topping Menu and check the pizza prices (at the bottom of that page); you may find it helpful to write these down. Then go to the Internet Pizza Server Ordering Area and create the pizza of your dreams!!

To Calculate the Cost of a Pizza:

Here is a "personal" pizza with pepperoni, mushroom and olives.

Let's suppose the base price was \$2.00 and each topping was \$.40, the total cost would be \$3.20:
 Total cost equals Base price plus Number of toppings times Price per topping: T = B + N * (P) \$3.20 = \$2.00 + 3 * (0.40)

Now calculate the cost of the Yummy Sample Pizza (a large with three toppings), then check your answer:

Cost Comparisons

To find the best "deal" on pizza, we have to be able to compare the prices for the different sizes. One way to do this is by calculating the "unit price" (like the price per pound, or cost per serving now listed in grocery stores).

Let's consider think of this snack-size pizza as ONE SERVING. Once we find the area of this pizza, we can use it as the base unit for determining the number of servings provided by the other pizzas.

We'll use the personal-size pizza as an example and go step-by-step through the procedure for calculating the area:

We can use the pixel width as the approximate diameter of the pizza. So, look at the picture of the pizza and find its width.
 width = 100
Then, since the radius of a circle equals one-half the diameter, we can divide the the pixel width by two to get a rough estimate of the radius.
 100 ÷ 2 = 50
Next, we "square" the radius (multiply it times itself).
 50 * 50 = 2500
Now multiply the radius squared times pi (in this case we'll multiply times three -- this is a bit less than the actual value of pi, but the width of the image was greater than the diameter so this will be balance out somewhat).
 2500 * 3 = 7500

 Area equals pi times the radius squared A = p * r2 A = p * 502 A = p * 2500
NOTE: p (pi pronouced like pie) is approximately equal to 22/7 (about 3.14); when estimating, "3" is close enough -- especially since the pixel width is a bit more than the pizza width.
 A = p * 2500 A = 3 * 2500 A = 7500

If we use the personal-size pizza as the base unit, then 7500 square pixels would be one serving (although we may want to think of it as 7500 crumbs per serving...) with a total cost of \$3.20 (for a personal-size pizza with three toppings).

Now determine the number of servings provided by each of the other size pizzas and check your answers. Remember, first find the area of the pizza:
A = p r2

and then divide by the amount in one serving (ie. 7500 crumbs per serving)

Real-World Application

Use the formula for the area of a circle to compare the costs of these pizzas (Based on prices in the Pittsburgh area):

A = p r2

NOTE: p (pi pronouced like pie) is approximately equal to 22/7 (about 3.14); when estimating, "3" is close enough.

 If a 10" Cheese Pizza costs \$5.55 and toppings are \$.75 each, how much would a 10" pizza with red peppers, bacon and green olives cost? click to check7.80 If a 14" plain cheeze pizza costs \$8.60 and toppings are \$1.10 each, how much would a 14" pizza with sausage, onion and mushrooms cost? click to check11.90 If a 16" Cheese Pizza costs \$10.55 and toppings are \$1.30 each, how much would a 16" pizza with black olives, pineapple and green peppers cost? click to check\$14.45

Extension

What do YOU think is a reasonable amount for a single serving?

Using this, select the best buy for pizza(s) with the toppings of your choice for your own family (you may do half-and -half, if you wish). Feel free to get "extra" so you can have it for breakfast, too....