SOLUTION: It is given that half the sum of the ages of a father and his son equals the difference between their ages. In 15 years' time, the father will be twice as old as his son. Given tha

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: It is given that half the sum of the ages of a father and his son equals the difference between their ages. In 15 years' time, the father will be twice as old as his son. Given tha      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 881578: It is given that half the sum of the ages of a father and his son equals the difference between their ages. In 15 years' time, the father will be twice as old as his son. Given that the father is x years old and his son is y years old.
(a) Form two equations connecting x and y.
(b) Solve these two simultaneous equations in (a) and find the ages of the father and that of the son.
My Workings:
(a) 1/2(x+y)=x-y
y+15=2(x+15)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It is given that half the sum of the ages of a father and his son equals the difference between their ages. In 15 years' time, the father will be twice as old as his son. Given that the father is x years old and his son is y years old.
(a) Form two equations connecting x and y.
1%2F2(x+y) = x - y
x + y = 2(x-y)
x + y = 2x - 2y
y + 2y = 2x - x
3y = x
and
x+15 = 2(y+15)
x + 15 = 2y + 30
x = 2y + 30 - 15
x = 2y + 15
:
(b) Solve these two simultaneous equations in (a) and find the ages of the father and that of the son.
Replace x with 3y in the above equation
3y = 2y + 15
3y - 2y = 15
y = 15 yrs is the son's age
then
x = 3(15)
x = 45 yrs is the father's age
:
:
You can confirm this in the given statements by replacing x and y