How many employees preferred the company's current benefit plan?

Question

A company recently surveyed all of it's employees. Overall, 3 out of every 16 employees preferred the company's current benefit plan. Additionally, 5 out of every 8 employees preferred a different benefit plan. A total of 150 employees did not indicate a preference for either the current benefit plan or a different benefit plan. How many employees preferred the company's current benefit plan?

Answer 1

Hi Bruce

 

You can look at the ratios that are given as fractions, such that 3/16 like the benefit plan; 5/8 or with a common denominator 10/16 prefer a different plan.  This means that 3/16 + 10/16 = 13/16 answered the survey.  This would mean that 3/16 did not respond with a preference which we are told is a total of 150 employees.  This is the same fraction of employees that preferred the benefit plan so the same number of employees (150) preferred the plan as did not indicate a preference.

Answer 2

Bruce, there is a deal that says a whole is made up of the sum of its parts.

 

3/16 of the people like the current plan, 5/8 like another, and 150 don't much care.

 

So, the 150 is the remaining fraction of those surveyed. 3/16 + 5/8 = 3/16 + 10/16 = 13/16

 

This means that the 150 is 3/16 of those surveyed. If I make 16 equal squares and 3 of them total 150, then one square is 50. Sixteen squares of 50 is 50 x 16 = 800 people surveyed.

 

Hope this helps!

Answer 3

x = total employees

 

3/16 x + 5/8 x = x - 150

 find common denominator

3/16 x + 10/16 x = x - 150

 

subtract x from both sides (remember x= 1x = 16/16x)

         13/16 x = x - 150           

       -16/16 x    -x

          -3/16x     =   -150

 

multiply by inverse

 (-16/3)(-3/16)x =   (-150)(-16/3)    

 

                   x = 800