SOLUTION: Twelve years ago my father was twice as old as I was, and three years ago our combined age was 108. How old is my father now?

Question 1150389: Twelve years ago my father was twice as old as I was, and three years ago our combined age was 108. How old is my father now?
Found 3 solutions by ankor@dixie-net.com, josmiceli, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
let f = father's present age
let y = your present age
:
Write an equation for each statement, simplify each equation
:
Twelve years ago my father was twice as old as I was,
f - 12 = 2(y-12)
f - 12 = 2y - 24
f = 2y - 24 + 12
f = 2y - 12
and three years ago our combined age was 108.
(f-3) + (y-3) = 108
f + y - 6 = 108
f + y = 108 + 6
f + y = 114
Replace f with (2y-12) from the 1st equation
(2y-12) + y = 114
3y = 114 + 12
3y = 126
y = 126/3
y = 42 is your age
then
f = 2(42) - 12
f = 84 - 12
f = 72 is father's age
:
:
Confirm that in statement:
"twelve years ago my father was twice as old as I was,"
72 - 12 = 2(42-12)
60 = 2(30)

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = my father's age now
Let = my age now
(1)
(2)
----------------------------------------
(1)
(1)
and
(2)
(2)
-------------------------------
add (1) and (2)
(1)
(2)
---------------------------

and
(2)
(2)
------------------------
My father is 72 now
------------------------
check:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Twelve years ago my father was twice as old as I was, and three years ago our combined age was 108. How old is my father now?

Let father's age be F, and my age, M
Then we get: F - 12 = 2(M - 12)____F - 12 = 2M - 24____F - 2M = - 12 ---- eq (i)
Also, since their ages summed to 108, 3 years ago, then now, their ages sum to 108 + 2(3) = 108 + 6 = 114
We then get: F + M = 114____M = 114 - F ------ eq (ii)
F - 2(114 - F) = - 12 ----- Substituting 114 - F for M in eq (i)
F - 228 + 2F = - 12
3F = 216
F, or father's age is:
That's ALL!!
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