A two-digit number has digit product 8. Adding 18 to the number reverses its digits. What is the number?

Problem restatement
Let the number be 10a + b with ab = 8 and 10a + b + 18 = 10b + a. Find the number.

Concept/Approach
Use the reversal equation to relate a and b; combine with the product condition to solve integer digits.

Step-by-Step calculation
10a + b + 18 = 10b + a ⇒ 9a − 9b = −18 ⇒ a − b = −2 ⇒ b = a + 2ab = 8 ⇒ a(a + 2) = 8Try digit possibilities: a = 2 ⇒ b = 4 works (2 × 4 = 8)Number = 24

Verification/Alternative
24 + 18 = 42, which is the reversal; product of digits = 8.

Common pitfalls
Taking a = 4, b = 2 (gives −2 = a − b = 2, contradiction).

Final Answer
24