SOLUTION: Six years ago John was four times as old as his sister Mary in four years time you will be twice as old as Mary how old are they now ?

Question 1091732: Six years ago John was four times as old as his sister Mary in four years time you will be twice as old as Mary how old are they now ?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52785) (Show Source): You can put this solution on YOUR website!
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Read your post.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Clearly you intended to say that in four years time John will be twice as old as Mary....

There are many different ways to start solving this problem using algebra; the different ways will take you down sometimes very different paths to the answer. For me personally, I prefer to use a single variable instead of two to solve a problem whenever it is practical.

So I would avoid the temptation to use two variables to represent John's and Mary's current ages (since that is what the problem asks for) and instead proceed as follows:

Let x = Mary's age 6 years ago
Then 4x = John's age 6 years ago

With those definitions, we know

x+10 = Mary's age 4 years from now; and
4x+10 = John's age 4 years from now

Then, since we are told that John will be twice as old as Mary 4 years from now,

So x = 5 is Mary's age 6 years ago, and 4x = 20 is John's age 6 years ago.

And so their current ages are 11 and 26.
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