Five years ago father was thrice son's age. 10 years hence father will be twice sons age, find present age ( use two variables)

f-5 = 3(s-5)

f + 10 = 2(s+10)
----------------
-15 = 3(s-5) - 2(s+10)

-15 = 3s - 15 -2s -20

20 = s
then
f-5 = 60 -15
f = 50

5 year ago.father age was9 time of his son.after 10 year from now father's age will be thrice of his son age.find the present of each one?

To solve this problem, let's assign two variables to represent the present ages of the father and the son.

Let's assume the present age of the son is 'x' years. Therefore, the present age of the father would be 'y' years.

According to the given information, five years ago, the father was thrice the son's age. This can be represented as:

y - 5 = 3(x - 5)

Similarly, 10 years from now, the father will be twice the son's age:

y + 10 = 2(x + 10)

Now we have a system of two equations:

1. y - 5 = 3(x - 5)
2. y + 10 = 2(x + 10)

We can solve this system of equations using substitution or elimination:

Using substitution method:

Rearrange equation 1 to express 'y' in terms of 'x':

y = 3(x - 5) + 5

Substitute this value of 'y' into equation 2:

3(x - 5) + 5 + 10 = 2(x + 10)

Simplify and solve for 'x':

3x - 15 + 5 + 10 = 2x + 20
3x = 2x + 20 + 10 - 5
3x - 2x = 25
x = 25

Now that we have the value of 'x', we can substitute it back into either equation to find 'y'. Let's use equation 1:

y - 5 = 3(25 - 5)
y - 5 = 3(20)
y - 5 = 60
y = 60 + 5
y = 65

Therefore, the present age of the son is 25 and the present age of the father is 65.