A number decreased by 30 is the same as 14 decreased by 3 times the number. Find the number. Explain!

Question

A number decreased by 30 is the same as 14 decreased by 3 times the number. Find the number. Explain!

Answer 1

The answer is 11.

 

x - 30 = 14 - 3x

     4x = 44

       x = 11

A number (x) decreased by 30 (x - 30) is the same as  (=) 14 decreased by 3 times the number (14 - 3x).

Answer 2

Let's call the unknown number x

 

Now let's decrease it by 30, that is x-30

 

Now let's write out "14 decreased by three times the number", that is 14 - 3x

 

The problem says these are the same, that is x - 30 = 14 - 3x

 

We now want to isolate, or solve for, x

 

Move the x to one side of the equation by adding 3x to both sides

 

3x + x -30 = 14 - 3x + 3x

 

4x -30 = 14

 

Now move the 30 to the right hand side by adding 30 to both sides

 

4x - 30 + 30 = 14 + 30

 

4x = 44

 

Now all we have to do to get x is divide both sides by 4

 

4x/4 = 44/4

 

x = 11