When a number is decreased by 20% of itself, the result is 104. What is the number?

Question

When a number is decreased by 20% of itself, the result is 104. What is the number?

Answer 1

The key to solving word (story) problems is to correctly translate the words and phrases into concise, precise math expressions (with variables and operations).

 

After reading and understanding the problem, assign variable(s).  If possible, try to assign a variable to the value the problem asks you to find.  In this problem, let x="the number"

 

Now, translate:

  "When a number is decreased by 20% of itself, the result is 104"  means

               x                 -                     0.20x                        =          104

 

       Notes:  "of" usually means multiply

         Percent can be written as  20%  or 0.20  or 20/100  as needed

 

  "What is the number?"    means    report x

 

O.K., the easy math:

          x - 0.2x = 104

             0.8x = 104          (collect terms)

                x = 130            (divide both sides by 0.8)

 

Checking (very important):

  Is   130 - 0.20(130 = 104   ?

        130 - 26 = 104    ?

           104 = 104   ?  yes.

Answer 2

First, think of 20% as one-fifth (1/5) of the original number, the one you want to find. When we subtract 20% - or one-fifth - from that number, the total is 104. Think of the original number as five-fifths (5/5) of itself.

 

Next, realize that five-fifths minus one-fifth is four-fifths: 5/5 - 1/5 = 4/5

 

It follows that 104 represents 4/5 of the original number.

 

Now, divide 104 by 4: 104/4 = 26. This result represents one-fifth of the original number, so we can either multiply it by 5 or we can add it to 104 to find the original number.

 

Either way you should get the same result, so try it both ways to check your work!