Please help answer this question.

Question

A company recently surveyed all of its 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

You're given the following:

 

3/16 prefer the current plan

5/8 prefer a different plan

150 people have no preference

 

The first step is to find a way to use the two fractions you're given to find the sum of all people with a preference.  To do this, you must find the greatest common denominator. 

 

If 5/8 is multiplied on top and bottom by 2, you'll have 10/16. 

 

5/8=10/16

 

To find the sum of those with an opinion, add 3/16 and 10/16. Since the denominators are the same, just add the numerator. 

 

3/16 + 10/16 = 13/16

 

This leaves 3/16 left who had no opinion.  

 

From here, you can logically deduce:

 

3/16 = 150 people without an opinion

 

Since we know 3/16 agreed to keep the current plan, this must also reflect that 150 people want to keep the current plan. 

Answer 2

3/16 prefer the company plan

5/8 prefer a different plan

3/16+5/8=3/16+10/16=13/16 prefer the company plan or a different plan

16/16-13/16=3/16 did not indicate a preference

150 did not indicate a preference

150=3/16 of what number ?

150=3/16*n

n=150*(16/3)

n=50*16

n=800 employees

3/16 preferred the company plan

3/16*(800)=3*50=150 preferred the company plan (but we already knew the answer because we found that 150 was 3/16 of 800 !)