SOLUTION: 6 yaers ago the age of father was 6 times the age of son. After 8 years the age of father will be twice the son. What are their present ages?

Question 189303: 6 yaers ago the age of father was 6 times the age of son. After 8 years the age of father will be twice the son. What are their present ages?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let f = father's present age
Let s = son's present age
:
Write an equation for each statement:
:
6 years ago the age of father was 6 times the age of son.
(f-6) = 6(s-6)
f - 6 = 6s - 36
f - 6s = -36 + 6
f - 6s = -30
:
After 8 years the age of father will be twice the son.
(f+8) = 2(s+8)
f + 8 = 2s + 16
f - 2s = 16 - 8
f - 2s = 8
:
Use elimination with these two equations:
f - 2s = 8
f - 6s = -30
-----------------subtraction eliminates f
+4s = 38
s =
s = 9.5 yrs is son's present age
:
Then
f - 2(9.5) = 8
f - 19 = 8
f = 27 yrs is father's present age
:
Usually solution to these problems are integers, however, let's check it:
check solution in the the statement:
"6 years ago the age of father was 6 times the age of son."
(27-6) = 6(9.5-6)
21 = 6(3.5)
21 = 21
and
"After 8 years the age of father will be twice the son. "
27 + 8 = 2(9.5 + 8)
35 = 2(17.5)
35 = 35
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