For nuclei, the radius-mass number relation is $R = R_0 A^{1/3}$ where $R$ is nuclear radius and $A$ is mass number.

For the first nucleus: $R_1 = 4.8\,\text{fm}, \quad A_1 = 64$ So, $4.8 = R_0 (64)^{1/3}$ Since $64^{1/3} = 4,$ we get $R_0 = \frac{4.8}{4} = 1.2\,\text{fm}$

For the second nucleus: $R_2 = 4\,\text{fm}$ Using $R_2 = R_0 A_2^{1/3},$ $4 = 1.2\, A_2^{1/3}$ Therefore, $A_2^{1/3} = \frac{4}{1.2} = \frac{10}{3}$

Cube both sides: $A_2 = \left(\frac{10}{3}\right)^3 = \frac{1000}{27}$ The question says mass number is $\frac{1000}{x}$, so $x = 27$

Final answer: $\boxed{27}$

Comparison with stored correct answer: Stored correct answer = 27, which matches the derived answer.