SOLUTION: I am three times as old as you were when I was as old as you are now. When you got to be my age together our ages will be 84. How old are we now?

Question 203238: I am three times as old as you were when I was as old as you are now. When you got to be my age together our ages will be 84. How old are we now?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I am three times as old as you were when I was as old as you are now.
When you got to be my age together our ages will be 84.
How old are we now?
:
Let x = my present age
Let y = your present age
then
(x-y) the difference in the ages
:
"I am three times as old as you were when I was as old as you are now."
x = 3[y - (x - y)]
x = 3(y - x + y)
x = 3(2y - x)
x = 6y - 3x
x + 3x = 6y
4x = 6y
:
" When you got to be my age together our ages will be 84."
x + x +(x-y) = 84
3x - y = 84
-y = -3x + 84
y = (3x - 84)
:
Substitute (3x-84) for y in the equation: 4x = 6y
4x = 6(3x-84)
4x = 18x - 504
504 = 18x - 4x
504 = 14x
x =
x = 36 is my age
then
4(36) = 6y
144 = 6y
y =
y = 24
:
Check solution
36 - 24 = 12 is the age difference
:
"I am three times as old as you were when I was as old as you are now."
36 = 3(24 - 12)
36 = 3(12)
:
"When you got to be my age together our ages will be 84.
36 + (36 + 12) = 84
:
I am 36 and you are 24

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