Final answer:
Zaida can spend her $90 on three types of pizzas in various combinations. By creating an inequality equation with variables representing the quantity of each pizza type and considering the cost of each, we systematically find all integer solutions that do not exceed her budget.
Step-by-step explanation:
Determining Combination Possibilities for Pizza Purchases
The question asks us to find out in how many different ways Zaida can spend her $90 on a combination of three pizza types priced at $6, $10, and $15. To solve this, we need to figure out all possible combinations of the three types of pizzas (pepperoni, Canadian bacon pineapple, and deluxe veggie) she can buy without exceeding her budget.
We can represent the number of each type of pizza purchased as variables: let's say 'p' for pepperoni, 'c' for Canadian bacon and pineapple, and 'v' for deluxe veggie. Using these variables, we can write the equation that represents all possible purchases:
6p + 10c + 15v ≤ 90.
This is a problem of combinatorics where we look for integer solutions to this linear inequality. We explore combinations with systematic trial and error, starting with the highest-priced pizza and working down to the lower-priced ones. Allowing for cases where Zaida might decide not to buy certain types of pizza (i.e., zero pizzas of that type), we will find the total number of possible combinations by considering all scenarios where the total cost does not exceed $90.
To avoid overcomplication, let's show an example:
Example:
If Zaida buys only deluxe veggie pizzas, she can buy at most 6 pizzas (6 x $15 = $90).
As there are numerous possibilities, following this process will eventually give us the total number of unique combinations Zaida could choose for her pizza party.