SOLUTION: John is now twice as old as he was when Mary was three years older than he is now, but he is only half as old as Mary is at present. Now, how old are they? I have tried 2x-3=1/2

Question 585255: John is now twice as old as he was when Mary was three years older than he is now, but he is only half as old as Mary is at present. Now, how old are they?
I have tried 2x-3=1/2x 1/2x times 3/2x=3 times 2/3 x=2
I don't know how else to do the problem I am at a complete loss of how to solve this. If you could help me that would be much appreciated. Thanks.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
John is now twice as old as he was when Mary was three years older than he is now,
but he is only half as old as Mary is at present. Now, how old are they?
:
Let j = J's present age
Let m = M's present age
Let d = m-j; the difference in their ages
:
"he is only half as old as Mary is at present.
j = .5m
:
"now twice as old as he was when Mary was three years older than he is now,"
j = 2(j+3-d)
j = 2j + 6 - 2d
j - 2j = 6 - 2d
-j = 6 - 2d
replace d with (m-j)
-j = -2(m-j) + 6
-j = -2m + 2j + 6
-j - 2j = -2m + 6
-3j = -2m + 6
-3j = -2m + 6
replace j with .5m
-3(.5m) =-2m + 6
-1.5m + 2m = +6
.5m = 6
m = 12 yrs is Mary's present age, then 6 yrs is John's age
:
:
See of that checks out
"John is now twice as old as he was when Mary was three years older than he is now(that's 9) ,
6 = 2(9 - 6)

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