Question

A teacher is ordering pizza for his students. He has two choices, pepperoni which costs $7 each and Cheese which costs $5 each. If the teacher cannot spend more than $70, which inequality represents all possible combinations of x pepperoni pizzas and y cheese pizzas?

Option 1: 7x + 5y ≤ 70
Option 2: 7x + 5y ≥ 70
Option 3: 7x - 5y ≤ 70
Option 4: 5x + 7y ≤ 70

Answer 1

The inequality to determine the combinations of pepperoni and cheese pizzas that can be ordered within a $70 budget is 7x + 5y ≤ 70, which is Option 1.

Step-by-step explanation:

The inequality that represents all possible combinations of x pepperoni pizzas and y cheese pizzas the teacher can order without exceeding a budget of $70 is 7x + 5y ≤ 70. This inequality, which is Option 1, is the correct representation because for each pepperoni pizza (x) the teacher spends $7 and for each cheese pizza (y) the teacher spends $5. The teacher's total expense should be less than or equal to $70.

Using the inequality, the teacher can calculate several combinations of the two types of pizzas where the total cost does not exceed the budget. For example, if the teacher wants to order 5 pepperoni pizzas, the equation would be 7(5) + 5y ≤ 70, which simplifies to 35 + 5y ≤ 70. Here, the maximum number of cheese pizzas (y) that could be purchased without going over the budget can be determined by solving for y.