Two-digit number with unit digit fixed: A two-digit number has 3 in the units place, and the sum of its digits equals one-seventh of the number itself. Find the number.

Introduction / Context:
This problem blends a fixed units digit with a proportional relation between the number and the sum of its digits. Representing the two-digit number algebraically lets us solve with a couple of steps.

Given Data / Assumptions:

• Let the tens digit be t.
• Units digit is 3.
• Sum of digits (t + 3) = (1/7) * (10t + 3).

Concept / Approach:
Express the number as 10t + 3. Use the given proportional relation to form and solve a simple linear equation in t. Confirm that the result yields a valid digit (0–9).

Step-by-Step Solution:

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

Why Other Options Are Wrong:

• 43, 53, 73, 83: Do not satisfy the proportional sum condition with units digit 3.

Common Pitfalls:
Accidentally using (1/7)*(sum of digits) = number. The statement says the sum equals one-seventh of the number, not the other way around.

Final Answer:
63