Question

1. construct arguments a survey found that 22% of high school students and 54% of teachers and school employees drive to school. the ratio of students to employees is about 10 to 1. roger states that the number of students who drive to school is greater than the number of teachers and employees who drive to school. explain how roger’s statement could be correct.

Explanation:

Step1: Define Variables

Let the number of employees be \( x \). Then the number of students is \( 10x \) (since the ratio of students to employees is 10 to 1).

Step2: Calculate Number of Drivers

• Number of student drivers: \( 22\% \) of \( 10x \) is \( 0.22\times10x = 2.2x \).
• Number of employee drivers: \( 94\% \) of \( x \) is \( 0.94x \).

Step3: Compare the Two Quantities

We compare \( 2.2x \) and \( 0.94x \). Since \( 2.2x>0.94x \) (because \( 2.2 > 0.94 \) and \( x>0 \) as it represents the number of employees), the number of student drivers is greater than the number of employee drivers. So Roger's statement can be correct because even though the percentage of student drivers is lower, the number of students is much larger (10 times the number of employees) and the product of the percentage and the number of students results in a larger number of drivers compared to the number of employee drivers.

Answer:

Roger's statement could be correct because if the number of students is 10 times the number of employees (from the 10:1 ratio), the number of student drivers (22% of 10 times the number of employees) is \( 2.2\times \) (number of employees) and the number of employee drivers is \( 0.94\times \) (number of employees). Since \( 2.2>0.94 \), the number of student drivers is greater.