Thursday, April 19, 2012

Thirty percent of a company's employees are over 50 years of age. If 450 people work at the same company, how many are over 50 years old?

This is a typical problem involving percents. There are a few different way to approach such problems. 


Recall that percent is a numerator (top) of a fraction with the denominator (bottom) equal to a 100. For example, 75% of something is equivalent to 75/100 of that number.


So, one way to solve a percent problem is by setting up a proportion:


Part/Whole = Percent(%)/100 


If 30% of all employees are over 50 years of age, then the ratio of the number of employees over 50 (unknown, or x) to the total number of employees (450) is 30%, or 30/100:


`x/450 = 30/100`


Proportions can be solved by cross-multiplying:


100x = 30*450


Dividing both sides by 100 results in x = 3*45 = 135 employees.


135 employees of the company are over 50 years old.


Alternatively, a percent formula can be used to solve this problem. It can be written as 


Part = p*Whole.


Here, p is the percent expressed as a decimal. In the given problem, p is 30% = 0.3. Part is the unknown number of employees over 50 years of age, and Whole is the total number of employees of the company, 450.


Therefore, Part = 0.3*450 = 135, which is the same as the result above.


The number of employees over 50 years of age is 135.

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