SOLUTION: The sum of a fathers age and his son son's age is 100 years. Also, one-tenth of the product of their ages, in years exceeds the father's age by 180. How old is the son ?

Question 638661: The sum of a fathers age and his son son's age is 100 years. Also, one-tenth of the product of their ages, in years exceeds the father's age by 180. How old is the son ?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Father's age =x
son's age = y
x+y = 100
x= 100-y
According to the second condition
(1/10) xy = x+180
xy= 10(x+180)
xy = 10x+1800
xy-10x=1800
x(y-10)=1800
x= 1800/(y-10)
100-y= 1800/(y-10)
(100-y)(y-10)=1800
100y-1000-y^2+10y=1800
y^2-110y+2800 =0
y^2-70y-40y+2800=0
y(y-70)-40(y-70)=0
(y-70)(y-40)=0
y= 70 OR 40
x+y = 100
son's age cannot be more than father's age
so y = 40
Son's age = 40 years
Fathers age = 60 years

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