A two-digit number has 3 as its units digit, and the sum of its digits equals one-seventh of the number itself. What is the number?

Introduction: Represent the number using its tens digit and the fixed units digit 3. The given condition links the sum of digits to one-seventh of the number, producing a simple linear equation in the tens digit.

Given Data / Assumptions:

• Number = 10t + 3.
• Sum of digits = t + 3 = (1/7)(10t + 3).
• Digits are 0–9 and t ≠ 0.

Concept / Approach: Multiply both sides to clear the fraction; solve for t. Substitute back to obtain the number and verify.

Step-by-Step Solution:

Verification / Alternative check: Sum of digits 6 + 3 = 9; one-seventh of 63 = 9, condition satisfied.

Why Other Options Are Wrong: 43, 53, 73, 83 do not satisfy the one-seventh condition.

Common Pitfalls: Forgetting to multiply both sides by 7 or miscomputing the sum of digits.

Final Answer: 63