Question

1. a large cheese pizza costs $7.50. diego has $40 to spend on pizzas. how many large cheese pizzas can he afford? explain or show your reasoning.

Explanation:

Step1: Define the problem

We need to find the number of pizzas \( n \) Diego can buy. The total money he has is \( \$40 \), and each pizza costs \( \$7.50 \). The formula for the total cost of \( n \) pizzas is \( \text{Total Cost} = \text{Cost per Pizza} \times n \). We need to find the largest integer \( n \) such that \( 7.50n \leq 40 \).

Step2: Solve for \( n \)

We can solve the inequality \( 7.50n \leq 40 \) for \( n \) by dividing both sides by \( 7.50 \):
\[
n \leq \frac{40}{7.50}
\]
Calculating \( \frac{40}{7.50} \), we get:
\[
\frac{40}{7.50} = \frac{400}{75} = \frac{16}{3} \approx 5.333\ldots
\]

Step3: Determine the number of pizzas

Since we can't buy a fraction of a pizza, we take the largest integer less than or equal to \( 5.333\ldots \), which is \( 5 \). We can also check: \( 5 \times 7.50 = 37.50 \), which is less than \( 40 \), and \( 6 \times 7.50 = 45 \), which is more than \( 40 \). So Diego can afford \( 5 \) pizzas.

Answer:

Diego can afford 5 large cheese pizzas.