Twenty less than 8 times a number is the same as 15 more than the number

The main part of solving this problem is carefully looking at each and every word of the problem very minutely. The details required for solving the problem is already given in the question.
Let us assume the unknown number to be = x
Then the equation for getting to the unknown number can be written as
8x - 20 = x + 15
8x - x = 15 + 20
7x = 35
x = 35/7
   = 5
So from the above deduction we can easily conclude that the unknown number in the question is 5.

If you would like to write the following in the math expression, you can do this using these steps:

a number ... n
twenty less than 8 times a number ... 8 * n - 20
is the same as ... =
15 more than the number ... n + 15

8 * n - 20 = n + 15
8 * n - n = 15 + 20
7 * n = 35    /7
n = 35 / 7
n = 5

The number we are looking for would be 5.