Jack is 2 2 times as old as Lacy. 7 7 years ago the sum of their ages was 13 13. How old are they now?
OK, there seems to be a bit of repitition in your question, so I'm going to reword it as follows.
Jack is 2 times as old as Lacy. 7 years ago the sum of their ages was 13. How old are they now?
Let Jack's age be X.
Let Lacy's age be Y.
Using the information given, we have
Jack is 2 times as old as Lacy: this means X = 2Y
7 years ago the sum of their ages was 13: Since Jack is now X years old, then 7 years ago his age would be (X - 7), So ...
7 years ago the sum of their ages was 13: This means (X - 7) + (Y - 7) = 13, or, X + Y - 14 = 13, i.e. X + Y = 27
Our two equations then are,
X = 2Y
X + Y = 27
Substituting for X = 2Y into the 2nd equation,
2Y + Y = 27
3Y = 27
Y = 9
X = 2Y = 18
This give the ages as: Jack is 18, Lacy is 9