A two-digit number has a tens digit that exceeds its units digit by 2. If the number equals seven times the sum of its digits, what is the units digit?

Explanation

Let the tens digit be 'a' and the units digit be 'b'. Given, a = b + 2. The number can be expressed as 10a + b, and it equals 7 times the sum of its digits: 10a + b = 7(a + b). Simplifying, we get 10a + b = 7a + 7b, which leads to 3a = 6b or a = 2b. Combining this with a = b + 2, we have 2b = b + 2, so b = 2. Therefore, the units digit is 2.