To find a fraction equivalent to \( 7:1 \) in the form \( 77: x \), you can set up a proportion:
\[ \frac{7}{1} = \frac{77}{x} \]
Now, cross-multiply:
\[ 7x = 77 \cdot 1 \]
This simplifies to:
\[ 7x = 77 \]
Now, solve for \( x \) by dividing both sides by 7:
\[ x = \frac{77}{7} = 11 \]
So, the blank should be filled with \( 11 \). Therefore, \( 77:11 \) is equivalent to \( 7:1 \).