SOLUTION: A company has 72 more female employees than male employees. If the company has a total of 180 employees, how many are female?

Hi there,

THE PROBLEM:
A company has 72 more female employees than male employees. If the company has a total of 180 
employees, how many are female?

SOLUTION:
I will show you a solution using one variable. It is also possible to solve this problem using two variables 
by writing a system of equations. Let me know if you would like to see that solution.

Let x be the number of female employees.

We need an expression for the number of male employees. Sometimes students have a hard time figuring 
out these types of expressions. I'll walk through the thinking process here.

We know that the total number of employees (male plus female) equals 180.
We also know that there are 72 more female than male.

For example:
If there are 80 female employees, there are 8 male employees because 80 is 72 more than 8.
If there are 82 female employees, there are 10 male employees because 82 is 72 more than 10.
If there are 102 female employees, there are 30 male employees because 102 is 72 more than 30.

Do you see the pattern here? 
Do you see that number of female employees minus 72 equals the number of male employees?

What if the number of female employees is x. Then the number of male employees is x minus 72, or x-72.

So the number of female employees is x.
The number of male employees is x-72.

The sum of the female employees and the male employees is 180, or
x + x - 72 = 180

Now solve for x. Combine like terms.
2x - 72 = 180

Add 72 to both side of the equation.
2x - 72 + 72 = 180 + 72

Combine like terms. (-72+72=0)
2x = 252

Divide both sides by 2
2x/2 = 252/2

Simplify. (2x/2=x)
x = 126

In the context of this problem, x = 126 means that there are 126 female employees.
Since there are x-72 male employees, we have 126-72 = 54 male employees.

Check your work.
Do 126 female employees and 54 male employees total  180 employees?
126 + 54 = 180 
180 = 180 Check!

So the answer to your problem is: There are 126 female employees.

Hope this helps. If you have questions about the solution, feel free to email me.

Mrs. Figgy
math.in.the.vortex@gmail.com