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
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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
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
