Question

One third the sum of 13 and a certain number is the same as 1 more than twice the number. Find the number?

(A) 6

(B) 5

(C) 4

(D) 3

Answer 1

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.