SOLUTION: My son is completely unclear how to solve this age problem. 4 years ago Tom was twice as old as John. 4 years from now, John will be 3/4 Tom's age. How old are they now?

Question 240593: My son is completely unclear how to solve this age problem.
4 years ago Tom was twice as old as John. 4 years from now, John will be 3/4 Tom's age. How old are they now?
Found 2 solutions by stanbon, College Student:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
4 years ago Tom was twice as old as John. 4 years from now, John will be 3/4 Tom's age. How old are they now?
---------------------------------------
Let Tom's age NOW be "t".
Let John's age NOW be "j".
--------------------------------
4 years ago Equation:
4 years ago Tom was twice as old as John.
(t-4) = 2(j-4)
----------------------
4 years from now Equation:
John will be (3/4) Tom's age.
(j+4) = (3/4)(t+4)
============================
So use those two equations to solve for "t" and for "j".
t-4 = 2j-8
j+4 = (3/4)t + 3
---------------------------
t = 2j-4
j = (3/4)t - 1
-----------------------
Substitute for "t" and solve for "j":
j = (3/4)(2j-4)-1
j = (3/2)j-3-1
(1/2)j = 4
j = 8 (John's age NOW)
----------------
Substitute into t = 2j-4 to solve for "t":
t = 2*8-4 = 12 (Tom's age NOW)
===============================================
Cheers,
Stan H.

Answer by College Student(505) (Show Source): You can put this solution on YOUR website!
This requires several steps, so fasten your seatbelts! :)
.
If Tom was twice John's age 4 years ago, then we can say that 4 years ago:
x = John
2x = Tom
.
However, this was four years ago. Thus, in order to bring them to their current ages, we will say:
x+4 = John
2x+4 = Tom
.
Now, the problem tells us that 4 years from now John will be 3/4 Tom's age. So, four years from now:
John will be = (x+4)+4
Tom will be = (2x+4)+4
.
Now we are ready to write our equation for when John will be 3/4 Tom's age:
John+4 = (3/4)Tom+4

.
Now figure out their ages (today):
Remenber x+4 is John and 2x+4 is Tom... so,
4+4=8 ...John
2*4+4 = 8+4 = 12 ...Tom
.
Check that John will be 3/2 Tom's age in 4 years.
Remember x+4+4 corresponds to John and [(3/2)(2x+4)] to Tom.
x+4+4=(3/4)(2x+4+4) ??
4+4+4=(3/4)(2*4+4+4)
12=(3/4)(16)
12=12
.
Done! :)
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