Question 1091732
<br>Clearly you intended to say that in four years time John will be twice as old as Mary....<br>
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.<br>
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:<br>
Let x = Mary's age 6 years ago
Then 4x = John's age 6 years ago<br>
With those definitions, we know<br>
x+10 = Mary's age 4 years from now; and
4x+10 = John's age 4 years from now<br>
Then, since we are told that John will be twice as old as Mary 4 years from now,<br>
{{{4x+10 = 2(x+10)}}}
{{{4x+10 = 2x+20}}}
{{{2x = 10}}}<br>
So x = 5 is Mary's age 6 years ago, and 4x = 20 is John's age 6 years ago.<br>
And so their current ages are 11 and 26.