Explanation:

- The average of the six integers is 48. Thus, the sum of all six integers is \(48 \times 6 = 288\).

- The average of the first five integers is 70% of the sixth integer. Let the sixth integer be \(x\).

- The average of the first five integers is \(\frac{288 - x}{5}\).

- According to the problem, \(\frac{288 - x}{5} = 0.7x\).

- Solving this equation:

$$288 - x = 3.5x$$

$$288 = 4.5x$$

$$x = \frac{288}{4.5} = 64$$

- Option:2 - 64 \(\textcolor{green}{\checkmark}\)