SOLUTION: when i was twice as old as you are now said Jane you were a third as old as i am now. Linda thought for a moment thats right she agreed and seven years ago you were 4 times as old

Question 625469: when i was twice as old as you are now said Jane you were a third as old as i am now. Linda thought for a moment thats right she agreed and seven years ago you were 4 times as old as i was.
how old is jane
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
jane is 27
linda is 12
here's how:
let x = jane's age now.
let y = linda's age now.
7 years ago, jane was 4 times linda's age.
equation for that is:
x-7 = 4*(y-7)
simplify to get:
x-7 = 4y-28
solve for x to get:
x = 4y-21
when jane was 2 times linda's age, linda was 1/3 * jane's age.
this happened k years ago (we use letter k because we don't know how many years ago at this point in time).
equation for this is:
x-k = 2y
y-k = x/3
solve both these equations for k to get:
k = x-2y
k = y-x/3
since both equations are equal to k, you can set the expressions on the right of each equation equal to each other to get:
x-2y = y-x/3
multiply both sides of this equation by 3 to get:
3x-6y = 3y-x
add 6y to both sides of this equation and add x to both sides of this equation to get:
4x = 9y
divide both sides of this equation by 4 to get:
x = 9y/4
you now have 2 equations for x.
you have:
x = 4y-21
x = 9y/4
since both equations are equal to x, you can set the expressions on the right of each equation equal to each other to get:
4y-21 = 9y/4
multiply both sides of this equation by 4 to get:
16y-84 = 9y
subtract 9y from both sides of this equation and add 84 to both sides of this equation to get:
7y = 84
divide both sides of this equation by 7 to get:
y = 12
you should be able to use any of the equations to solve for x to get x = 27.
the one i used was the original one of:
x = 4y-21
this yielded x = 27
x = 9y/4 yielded x = 27 also.
you have x = 27 and y = 12
that's your answer.
to confirm, do the following from the original problem statement of:
when i was twice as old as you are now said Jane you were a third as old as i am now. Linda thought for a moment thats right she agreed and seven years ago you were 4 times as old as i was.
jane is 27
linda is 12.
7 years ago jane was 20 and linda was 5 which made jane 4 times as old as linda.
jane was twice as old as linda is now when jane was 24.
that was 3 years ago.
3 years ago, linda was 9 and and jane was 24 which made linda 1/3 as old as jane.
all portions of the problem statement check out so the answer is good.
CORRECTION TO PREVIOUS STATEMENT
3 years ago jane was 24 which is 2 times as old as linda is now (12).
3 years ago linda was 9 which is 1/3 times as old as jane is now (27).
answer is correct but last statement might have been confusing and so was corrected.

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