Explanation:

- The sum of the three numbers is given as 777.

- The ratio between the first two numbers is 7:9.

- This implies if the first number is 7x, the second is 9x.

- The ratio between the second and third numbers is 3:7.

- This implies if the second number is 3y, the third is 7y.

- Equating second numbers: 9x = 3y or y = 3x.

- The numbers can be represented as: 7x, 9x, and 7*(3x) = 21x.

- Their sum: 7x + 9x + 21x = 777.

- Simplified: 37x = 777 or x = 21.

- The second number is 9x = 9*21 = 189.

Option 3: 189