Question

A class consists of 1/5 freshmen, 3/5 sophomores, and 1/10 juniors; the rest are seniors. what fraction of the class is seniors?

Answer 1

Let us consider the total number of people in the class as 1

Total number of freshmen = 1/5

Total number of sophomores = 3/5

Total number of juniors = 1/10

Let us consider the total number of seniors as x.

Therefore,

Freshmen + Sophomores + Juniors + Seniors = Total number of students in a class

=> 1/5 + 3/5 + 1/10 + x = 1

=> 9/10 + x = 1

=> x = 1 - 9/10

=> x = 1/10

Thus, the number of seniors in the class is 1/10

Answer 2

The sum of freshmen, sophomores, juniors and seniors must be 1, because 1 corresponds to 100%, then we can write:

`(1)/(5)+(3)/(5)+(1)/(10)+x=1`

where x denotes the seniors. This last equation is equivalent to

`(4)/(5)+(1)/(10)+x=1`

Now, we will add the fraction on the left hand side,

`(4)/(5)+(1)/(10)=(8)/(10)+(1)/(10)=(9)/(10)`

then, our equation is

`(9)/(10)+x=1`

By moving 9 over 10 to the right hand side, we get

`x=1-(9)/(10)`

then, x is given by

`\begin{gathered} x=(10)/(10)-(9)/(10) \\ x=(1)/(10) \end{gathered}`

then, the fraction of seniors is 1/10