Two-digit number with a ratio condition: In a two-digit number, the units digit is three times the tens digit, and the sum of the digits is 8. What is the number?

Introduction / Context:This is a straightforward two-digit algebra problem involving a ratio between digits and a sum constraint. Setting variables for the tens and units digits allows a quick solution with substitution.

Given Data / Assumptions:

• Tens digit = t
• Units digit = 3t
• Sum of digits = t + 3t = 8

Concept / Approach:Use the sum condition to find t, then construct the number 10t + (3t). Ensure that 3t is a valid single digit (0–9), which it is once we compute t.

Step-by-Step Solution:

Verification / Alternative check:Check conditions: units is three times tens (6 = 3*2) and sum 2 + 6 = 8. Both satisfied.

Why Other Options Are Wrong:

• 20, 13: Do not satisfy units = 3*tens.
• 39, 62: Do not satisfy the sum of digits = 8 with the given ratio.

Common Pitfalls:Mixing up tens and units or writing the number as 3t*10 + t. Carefully map tens to the 10s place and units to the 1s place.

Final Answer:26