how many people wanted there benefits?

Question

A business did a survey of all its employees, 3 of 16 people wanted their benefits. 5 of 8 people wanted to change the benefits. Overall 150 didn't decide on the benefits.

Answer 1

This is a fraction problem combined with set theory.
3/16 wanted benefits
5/8 wanted to change benefits
let x be the fraction of people who did not decide on benefits

 

3/16 + 5/8 + x = 1

x = 1- 5/8 - 3/16

= 1 - 10/16 - 3/16

= 16/16 - 13/16

= 3/16

We also know that x is actually 150 people. And x = 3/16 of population.

It just happens 3/16 is also the fraction of people that want their benefits too.

So the number of people who wanted their benefits(3/16) is 150 also, because the number of people who did not decide on their benefits(3/16) was 150.

Answer 2

3/16 of the people wanted their benefits

5/8 = 10/16 of the people wanted to change the benefits

 

The only other possibility is the people that didn't decide on the benefits.  These three possibilities must add up to 1 since the business surveyed all its employees.  Therefore 

 

3/16 + 10/16 + (fraction that didn't decide) = 1

 

So the fraction that didn't decide on the benefits is 3/16, which is 150 people.  

 

So 150 people wanted their benefits.