To find the number that makes the ratio 10:x equivalent to 90:81, we can set up a proportion:
\[ \frac{10}{x} = \frac{90}{81} \]
Next, we can cross-multiply:
\[ 10 \cdot 81 = 90 \cdot x \]
Calculating the left side:
\[ 810 = 90x \]
Now, divide both sides by 90 to solve for \( x \):
\[ x = \frac{810}{90} \]
Calculating the right side:
\[ x = 9 \]
Thus, the number that makes the ratio equivalent to 90:81 is \( \boxed{9} \).