Question 324481
Five years ago father's age was seven times his sons age. Ten years hence their ages will be in the ratio of 5 : 2. Find their present ages 
Let x = father's age
and y = son's age
.
From:"Five years ago father's age was seven times his sons age."
x-5 =7(y-5) 
x-5 =7y-35 
x-7y = -30   equation 1
.
From:"Ten years hence their ages will be in the ratio of 5 : 2."
(x+10)/(y+10) = 5/2
2(x+10) = 5(y+10) 
2x+20 = 5y+50
2x-5y = 30   equation 2
.
x-7y = -30
2x-5y = 30
.
Multiply the top equation by -2 and add to the second:
-2x+14y = 60
 2x-5y = 30
-------------
    9y = 90
y = 10 years old (son's age)
.
Father's age:
x-7y = -30
x-7(10) = -30
x-70 = -30
x = 40 years old (father's age)