Alright, lets get started.
Suppose Pat's current age= x
Suppose his son Patrick's current age = y
Given that Pat is 25 years older than his son patrick, means
[tex] x = y + 25 [/tex] .......................................equation (1)
After 7 years Pat's age will be = (x+7)
After 7 years Patrick's age will be = (y+7)
After 7 years pat will be twice as old as patrick.
[tex] (x+7) = 2 (y+7) [/tex] ...............................equation (2)
From equation (1), putting the value of x in equation (2)
[tex] (y+25 + 7) = 2(y+7) [/tex]
[tex] y + 32 = 2y + 14 [/tex]
Subtrating y in both sides
[tex] y + 32 - y = 2y + 14 - y [/tex]
[tex] 32 = y + 14 [/tex]
Subtrating 14 in both sides
[tex] 32 - 14 = y + 14 - 14 [/tex]
y = 18
Hence
[tex] x = y + 25 = 18 + 25 = 43 [/tex]
It means Pat's age is 43 and Patrick's age is 18. : Answer
Hope it will help :)
