A sample of copper contains two isotopes, 63Cu and 65Cu. If the relative atomic mass of this copper sample is 63.55, what is the percentage abundance of the 63Cu isotope?

Let $x$ be the percentage abundance of $^{63}$Cu.
Then the percentage abundance of $^{65}$Cu will be $(100 - x)$.
The relative atomic mass is calculated as:

$$\text{Relative Atomic Mass} = \frac{(\text{mass of isotope 1} \times \text{abundance of isotope 1}) + (\text{mass of isotope 2} \times \text{abundance of isotope 2})}{100}$$

Substitute the given values:

$$63.55 = \frac{(63 \times x) + (65 \times (100 - x))}{100}$$

Multiply both sides by 100:

$$63.55 \times 100 = 63x + 65(100 - x)$$ $$6355 = 63x + 6500 - 65x$$

Combine the $x$ terms:

$$6355 = 6500 - 2x$$

Subtract 6500 from both sides:

$$6355 - 6500 = -2x$$ $$-145 = -2x$$

Divide by -2:

$$x = \frac{-145}{-2}$$ $$x = 72.5$$

The percentage abundance of the $^{63}$Cu isotope is $72.5\%$.

The percentage abundance of the $^{63}$Cu isotope is \boxed{\text{72.5%}}.