SOLUTION: Two years ago, a father was 8 times as old as his son. Ten years from now, the ratio of their ages will be 10:3. What is the father's age today? Thanks.

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Question 602276: Two years ago, a father was 8 times as old as his son. Ten years from now, the ratio of their ages will be 10:3. What is the father's age today?
Thanks.
Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"Two years ago, a father was 8 times as old as his son" ___ f - 2 = 8(s - 2) ___ f = 8s - 14

"Ten years from now, the ratio of their ages will be 10:3" ___ (f + 10) / (s + 10) = 10 / 3 ___ 3f + 30 = 10s + 100

multiplying 1st equation by 10 ___ 10f = 80s - 140

multiplying 2nd equation by 8 ___ 24f + 240 = 80s + 800

subtracting equations ___ 24f + 240 - 10f = 80s + 800 - 80s - -140 ___ 14f + 240 = 940

Answer by ankor@dixie-net.com(22740) About Me  (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:
:
"Two years ago, a father was 8 times as old as his son."
f - 2 = 8(s-2)
f - 2 = 8s - 16
f = 8s - 16 + 2
f = 8s - 14
:
" Ten years from now, the ratio of their ages will be 10:3."
%28%28f%2B10%29%29%2F%28%28s%2B10%29%29 = 10%2F3
cross multiply
3(f+10) = 10(s+10)
3f + 30 = 10s + 100
3f = 10s + 100 - 30
3f = 10s + 70
Replace f with (8s-14)
3(8s-14) = 10s + 70
24s - 42 = 10s + 70
24s - 10s = 70 + 42
14s = 112
s = 112/14
s = 8 yrs is son's age
then
f = 8(8) - 14
f = 64 - 14
f = 50 yrs is father's age today