Let's denote the unknown number as \( x \). According to the problem, we can set up the following equation based on the information given:
\[ \frac{35 + x}{4} = 2x \]
Now, we will eliminate the fraction by multiplying both sides of the equation by 4:
\[ 35 + x = 8x \]
Next, we will isolate \( x \) by moving \( x \) to the right side of the equation:
\[ 35 = 8x - x \]
This simplifies to:
\[ 35 = 7x \]
Now, we divide both sides by 7 to solve for \( x \):
\[ x = \frac{35}{7} = 5 \]
Thus, the number is:
\[ \boxed{5} \]
To verify, we can substitute \( x = 5 \) back into the condition of the problem:
\[ \frac{35 + 5}{4} = \frac{40}{4} = 10 \]
And double the number \( 5 \):
\[ 2 \times 5 = 10 \]
Since both results are equal, our solution \( x = 5 \) is correct.