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?
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A20
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B26
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C39
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D13
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E62
Answer
Correct Answer: 26
Explanation
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:
t + 3t = 8 ⇒ 4t = 8 ⇒ t = 2Units digit = 3t = 6Number = 10t + 3t = 20 + 6 = 26Verification / 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