#### Answer

The number we need to find is 8.

#### Work Step by Step

Let X be the number that we need to find.
One subtracted from nine times a certain number means 9X - 1.
15 added to seven times the number means 7X + 15.
Since both of these expressions are the same, we solve the following equation:
9X - 1 = 7X + 15
2X - 1 = 15
2X = 16
Divide both sides by 2.
X = 8
The number is 8.