Let the certain number be represented by \( x \).
According to the problem, one third the sum of 13 and the number can be expressed as:
\[ \frac{1}{3}(13 + x) \]
We are also told this is equal to 1 more than twice the number:
\[ 2x + 1 \]
Putting these two expressions together, we have the equation:
\[ \frac{1}{3}(13 + x) = 2x + 1 \]
To eliminate the fraction, we can multiply both sides of the equation by 3:
\[ 13 + x = 3(2x + 1) \]
Expanding the right side:
\[ 13 + x = 6x + 3 \]
Next, we can rearrange the equation to isolate \( x \). We begin by subtracting \( x \) from both sides:
\[ 13 = 6x - x + 3 \]
Simplifying gives:
\[ 13 = 5x + 3 \]
Now, subtract 3 from both sides:
\[ 13 - 3 = 5x \]
This results in:
\[ 10 = 5x \]
Next, we divide both sides by 5:
\[ x = 2 \]
Now that we have found \( x \), we check if it is equal to any of the provided answer options:
- (A) 6
- (B) 5
- (C) 4
- (D) 3
None of these options match \( x = 2 \). Thus, we conclude that none of the provided options are correct.
If we double-check the main equation with the value we calculated:
Substituting \( x = 2 \):
Left side:
\[ \frac{1}{3}(13 + 2) = \frac{1}{3}(15) = 5 \]
Right side:
\[ 2(2) + 1 = 4 + 1 = 5 \]
Both sides are equal. This confirms \( x = 2 \) works for the equation, but it appears to be an oversight in the problem options.
Thus, the answer is \( x = 2 \), which is not listed among the options provided.
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