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(52784) (Show Source):
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.
