SOLUTION: My son my father and I were all born on fathers day. When my son was born I was 3/7 the age of my father. Today my son is the age I was when he was born; in four years he will be

Question 984881: My son my father and I were all born on fathers day. When my son was born I was 3/7 the age of my father. Today my son is the age I was when he was born; in four years he will be exactly 1/3 the age of my father. how old was I when my son was born?
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
My son my father and I were all born on fathers day.
Let y = your age
let f = father's age
let s = son's age
:
When my son was born I was 3/7 the age of my father.
y - s = (f-s)
Multiply equation by 7
7(y - s) = 3(f - s)
7y - 7s = 3f - 3s
7y - 7s + 3s = 3f
7y - 4s = 3f
:
Today my son is the age I was when he was born;
s = y
multiply equation by 2
2s = y
:
in four years he will be exactly 1/3 the age of my father.
s + 4 = (f+4)
multiply equation by 3
3(s + 4) = f + 4
3s + 12 = f + 4
3s = f + 4 - 12
3s = f - 8
:
In the first equation, 7y - 4s = 3f, replace y with 2s
7(2s) - 4s = 3f
14s - 4s = 3f
10s = 3f
s = f
we can write it
s = .3f
:
in the third equation, 3s = f - 8, replace s with .3f
3(.3f) = f - 8
.9f = f - 8
8 = f - .9f
8 = .1f
f = 8/.1
f = 80 yrs is Dad's age
then
s = .3f
s = .3(80)
s = 24 yrs is son's age
and
y - 2s
y = 2(24)
y = 48 yrs is his age
:
how old was I when my son was born? that would be 24 yrs ago
48 - 24 = 24yr old when your son was born

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If they were all born on the same day of the year,
then the differences in their ages are integers
( whole numbers )
--------------------
Let = my age now
Let = my son's age now
Let = my father's age now
-----------------------------
"Today my son is the age I was when he was born"
My age when my son was born is:

"Today my son is the age I was"

(1)
-------------
"In four years he will be exactly 1/3 the age of my father."
(2)
-------------------------
Also:
"When my son was born I was 3/7 the age of my father."
As already shown, I was years old when my
son was born, so
(3)
( note that I have to subtract my son's age from
my father's age also )
-----------------------
(1), (2), and (3) are 3 equations with 3 unknowns,
so it's solvable
-----------------
(2)
(2)
(2)
-------------------
(3)
(3)
(3)
------------------------
By substitution:
(3)
and
(3)
(3)
(3)
----------------
(2)
(2)
(2)
----------------
(3)
(3)
(3)
(3)
-----------------
I was when my son was born

I was 24 yrs old when my son was born
-------------------
check:
When my son was born I was 3/7 the age of my father.

Today my son is the age I was when he was born

In four years he will be exactly 1/3 the age of my father.
(2)
(2)
(2)
(2)
OK

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