Solution:

Let's assume the present ages of the three persons as x, y, and z respectively.

According to the given information, the sum of their ages is 150 years.

Therefore, we can write the equation as:
x + y + z = 150 ---(1)

We are also given that 10 years ago, their ages were in the ratio 7:8:9.

Let's calculate their ages 10 years ago:

Age of the first person 10 years ago = x - 10
Age of the second person 10 years ago = y - 10
Age of the third person 10 years ago = z - 10

According to the given ratio, we can write the equation as:
(x - 10) : (y - 10) : (z - 10) = 7 : 8 : 9

Cross multiplying, we get:
7(y - 10) = 8(x - 10)
8(x - 10) = 9(z - 10)

Simplifying the equations, we get:
7y - 70 = 8x - 80 ---(2)
8x - 80 = 9z - 90 ---(3)

Now, we have three equations (1), (2), and (3) with three variables (x, y, and z). We can solve these equations simultaneously to find the values of x, y, and z.

Let's solve equations (2) and (3) to eliminate x:

7y - 70 = 8x - 80
8x - 80 = 9z - 90

Multiplying the second equation by 7, we get:
56x - 560 = 63z - 630

Now, let's solve equations (1) and (3) to eliminate z:

x + y + z = 150
8x - 80 = 9z - 90

Multiplying the first equation by 8, we get:
8x + 8y + 8z = 1200

Simplifying the equations, we get:
56x - 63z = -70
8x + 8y + 8z = 1200

Now, we have two equations (56x - 63z = -70) and (8x + 8y + 8z = 1200) with two variables (x and z). We can solve these equations simultaneously to find the values of x and z.

Let's solve these equations:

From equation (1), we can write x = 150 - y - z

Substituting the value of x in equation (56x - 63z = -70), we get:
56(150 - y - z) - 63z = -70

Simplifying the equation, we get:
8400 - 56y - 56z - 63z = -70
8400 - 56y - 119z = -70
-56y - 119z = -8470

Dividing the equation by -7, we get:
8y + 17z = 1210 ---(4)

Substituting the value of x in equation (8x + 8y + 8z = 1200), we get:
8(150