When a number is divided by 3, the result is the same as when the number is decreased by 10. What is the number?

Write two expressions and set them equal to each other.

Our first expression can be determined by understanding the line "a number is divided by 3". We can represent the number as #n#, and being divided by 3 is the same thing as #div 3#. So this particular expression will be #n div 3#.

The second expression can be determined by understanding the line "the number is decreased by 10". Once again, the number can be represented as #n# and since it is being decreased by 10, we know that it is subtracting by 10. So this particular expression can be #n - 10#.

Since it says that #n div 3# is the same as #n - 10#, we can know that they are equal to each other.
#n div 3 = n - 10#

We would want to isolate #n# and to do that I prefer that we multiply both sides by 3 to get rid of #div 3#.
#3(n div 3) = 3(n- 10)#
#n = 3n - 30#

Let's bring #3n# to the other side of the equal sign to separate the unlike terms from each other.
#n - 3n = 3n - 3n - 30#
#-2n = -30#
#n = 15#

Let's check whether the number is 15.
#15 div 3 = 15 - 10#
#5 = 5#

This is correct!

Answer: the number is 15