4) Mendoza's Pizzeria offers many wonderful topping options on their world-famous pizza pies. A cheese pizza costs $20, plus it costs $1 for any veggie topping (onions, green peppers, spinach, etc), and $2 for any meat topping (pepperoni, bacon, sausage, etc.). There must be at least 2 toppings on each pizza pie, but there cannot be more than 10 toppings on any one pie. Marty enters the scene with $30 in his pocket. a. Write a system of inequalities that represents the constraints on the number of each topping that can be included on Marty's pizza.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
a. Let the number of veggie toppings be x and the number of meat toppings be y.
For atleast 2 toppings, the inequality is .
For not more than 10 toppings, the inequality is .
Hence, the system of inequalities is and .
As cheese pizza costs $20, $1 for each veggie topping and $2 for each meat topping.
Marty's pocket has $30.
Step by step
Solved in 2 steps
