SOLUTION: Ten years ago a father was seven times as old as his son, two years hence twice his age will be equal to five times his sons. what is the present age of son?

Question 315459: Ten years ago a father was seven times as old as his son, two years hence twice his age will be equal to five times his sons. what is the present age of son?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Ten years ago a father was seven times as old as his son,
two years hence twice his age will be equal to five times his sons.
what is the present age of son?
:
Write an equation for each statement, simplify:
"Ten years ago a father was seven times as old as his son,"
f - 10 = 7(s-10)
f - 10 = 7s - 70
f = 7s - 70 + 10
f = 7s - 60
:
"two years hence twice his age will be equal to five times his sons."
2(f + 2) = 5(s+2)
2f + 4 = 5s + 10
2f = 5s + 10 - 4
2f = 5s + 6
:
what is the present age of son?
Replace f with (7s-60) in the above equation:
2(7s - 60) = 5s + 6
14s - 120 = 5s + 6
14s = 5s + 6 + 120
14s - 5s = 126
9s = 126
s =
s = 14 yrs, son's present age
:
:
Check solution, find father's age
f = 7s - 60
f = 7(14) - 60
f = 98 - 60
f = 38 yrs, father's age
:
"Ten years ago a father was seven times as old as his son, "
38 - 10 = 7(14-10)
28 = 7(4)
and
"two years hence twice his age will be equal to five times his sons."
2(38+2) = 5(14 + 2)
80 = 5(16); confirms our solution
:

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