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 son's age. What are their present ages?

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Question 190312: 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 son's age. What are their present ages?
Answer by ankor@dixie-net.com(22740) (Show Source):
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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 son's age.
What are their present ages?
:
Let f = father's present age
Let s = son's present age
:
Write an equation & simplify, for each statement:
:
"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 son's age."
2(f + 2) = 5(s + 2)
2f + 4 = 5s + 10
2f = 5s + 10 - 4
2f = 5s + 6
:
What are their present ages?
Substitute (7s-60) for f in the above equation:
2(7s - 60) = 5s + 6
14s - 120 = 5s + 6
14s - 5s = 6 + 120
9s = 126
s =
s = 14 yr's is son's present age
:
find f using eq: f = 7s - 60
f = 7(14) - 60
f = 98 - 60
f = 38 yrs is father's present age
:
:
Check solution's in the statement:
"two years hence twice his age will be equal to five times his son's age."
2(38+2) = 5(14+2)
2(40) = 5(16)