How many students have piercings both on their ears and their noses?

Question

In a class of 30 students, everyone has either a pierced nose or a pierced ear. The professor asks everyone with a pierced nose to raise his or her hand. Seven hands go up. Then the professor asked everyone with a pierced ear to do likewise. This time there are 26 hands raised. How many students have piercings both on their ears and their noses?

Answer 1

Let X represent the number of students that have BOTH ear and nose piercing.

 

7 have nose and possibly ear pierced, so 7-X of them have only nose pierced.

 

Likewise, 26 have ears and possibly nose pierced, so 26-x of them have only ears pierced.

 

There are 30 altogether.

 

So     # with only nose pierced + # with BOTH nose and ears pierced + # with only ears pierced = 30

                        7-X                +                      X                             +                26-X              = 30

 

            33 - x = 30    <--- combining like terms

            33 - x - 30 = 0 <--- solving for X

             3 - x = 0

             3 = x

              x = 3

  

 4 students have only nose pierced

23 student have only ears pierced

 3 have both nose and ears pierced

 

the total is 30.

 

Final answer is 3