Questions: At a particular college, 85% of the undergraduates are female. If 3485 women attend the college, how many total undergraduates attend the college? The total number of undergraduates is

At a particular college, 85% of the undergraduates are female. If 3485 women attend the college, how many total undergraduates attend the college?

The total number of undergraduates is

Transcript text: At a particular college, $85 \%$ of the undergraduates are female. If 3485 women attend the college, how many total undergraduates attend the college? The total number of undergraduates is $\square$

Solution

Solution Steps

To find the total number of undergraduates, we can use the given percentage of female students. If 85% of the undergraduates are female and there are 3485 female students, we can set up an equation to solve for the total number of undergraduates.

Let $ x $ be the total number of undergraduates.
Since 85% of $ x $ is 3485, we can write the equation: $ 0.85x = 3485 $.
Solve for $ x $ by dividing both sides by 0.85.

Step 1: Set Up the Equation

Given that $85\%$ of the undergraduates are female, and there are 3485 female students, we can express this relationship as: \[ 0.85x = 3485 \] where $x$ is the total number of undergraduates.

Step 2: Solve for Total Undergraduates

To find $x$, divide both sides of the equation by 0.85: \[ x = \frac{3485}{0.85} \]

Step 3: Calculate and Round

Calculate the value: \[ x = 4100 \]