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Click HERE to see what you will learn from this activity. |
Young Garzon Zifferelli owns and operates the best little pizza shop in all of Amish country. He is famous for pizza that leaves your mouth dripping with savory juices and your body begging for "just one more piece." Now Garzon's fame comes from his CRUSTS! He includes several secret ingredients that he has vowed will never be revealed to ANYONE, not even his mother. He is firmly convinced that the key to his success is guarding that recipe to the extreme. He won't let his employees mix up any dough. He does it himself, every day, behind locked doors. Garzon has an industrial strength dough maker that will make up to a maximum of 30 pounds of dough. |
Garzon sells two sizes of pizza,
large and small. The large size requires two full pounds of dough and
the small size takes one pound of dough.
So if you let x stand for the number of large pizzas and
y stand for the number of small pizzas, then the inequality
2x + y <= 30 mathematically describes how many pizzas of each
size Garzon's dough machine can produce.
SO HERE IS YOUR CHALLENGE:
Find all the different combinations of these two sized pizzas that Garzon's machine can make? Represent all of the possible answers on a coordinate grid.
HOW TO START:
Find pairs of numbers that indicate how many of each size pizza could be made from a single use of the machine. For example, Garzon certainly could make one large and one small, or five large and three small pizzas. He would not be using his machine at its maximum capacity, but he could do it. Use colored dots to represent these pairs of numbers on your graph.Now there are also some combinations that simply could not work because he wouldn't have enough dough. For example, he could not make 31 small pizzas and no large pizzas, because the machine only makes 30 pounds of dough. Choose a different color of dot on your graph to represent the combinations that wont work.
This problem will generate A LOT OF DOTS! You will need to determine how big your x and y axes should be to accommodate all the possible dots. Figure out the maximum number of large pizzas he can make. Your x axis must be at least that long. Then figure out the maximum number of small pizzas he can make. Your y axis will need to extend at least that far. (This activity is easier if you use an interval of one pizza per block on your graph paper.)
TO SET YOURSELF ABOVE THE REST:
STAR on your graph all the possible combinations that would indicate that the machine is being used at its maximum capacity. (You will recognize a pattern here if you do it correctly.)
When you are finished click here to compare your graph to ours, but remember, they might not be exactly the same if you used a different scale than we did.
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