Question

You and two friends each agree to drive \(\frac{1}{3}\) of a 75 -mile trip. Which equation would you use to find the number of miles each of you must drive? A. \(3 x=75\) B. \(\frac{1}{3} x=75\)

Short answer

Option A, \(3x = 75\), would be used to determine the distance each individual drives.

Step-by-step solution

Understand the Problem

Appreciate that the trip is 75 miles long and that it is divided equally among three people. That means that each individual drives the same distance.

Apply Mathematical Reasoning

To calculate the distance traveled by each person, the total miles (75 miles) should be divided by the number of people (3). This can be represented in algebraic terms as: \( x = \frac{75}{3} \), where 'x' is the miles each person has to drive.

Identify the Correct Equation

Looking at the options provided, only option A represents the given situation mathematically correct. Thus, the equation that would be used to compute the distance each person drives is \(3x = 75\). The \(3x\) in this equation stands for the contribution of each individual, and the equal to 75 signifies the total miles to be traveled.