Bootcamp Math problem

[sexysummer]

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Earl and Debbie are brother and sister. In 2020 Earl will be as old as his
father was when Earl was born. In 2010 Debbie was half as old as her father was
in 2004. How much older is Debbie than Earl?

the solution is kind of vague to me.
Earl's age is represented by X
Father's age in 2020 will be 2X (why is this twice Earl's age and how do I know)
Father's age in 2004 will be 2X-16 that's because 2020-2004 is 16 years ago---make sense, OK

in 2010 Debbie's age will be half her dad age in 2004 which is 0.5(2X-16) = x-8
10 years later after 2010, the age of Debbie will be
(X-8) + 10 = x + 2
the difference in age will be (x + 2) - x which is equal to 2

The only part I don't understand is in BOLD

please explain.

 

[LuckBloodandSweat]

Hey, I know this is really late and it might not help you now but I have an explanation that will make this easier to do for people in the future. I think using the algebra way is annoying but I kind of get why now.
Ok so Earl in 2020 is the same age as when his dad was when his mother gave birth to him. Think of it like this, I'm going to use random numbers to show that his dad has to be twice has age in 2020.

Let's say my dad was 36 years old when I was born. When I turn 36, he is 72 but 36 years ago he was 36! This will work for any pair of numbers because to be the same age as your dad was he'd have to be twice your age now.
In this question, you don't have any exact numbers to work with but if you understand that his father has to be twice his age you can just make up a number for the father's age in 2004 and stick with it. I got this wrong on Bootcamp too but I understand why now.
Lets say in 2004 the Father is 30 years old. That means Debbie is 15 years old in 2010. She is 25 years old in 2020 and the Father is 46 years old. Since Earl is half his father's age, he has to be 23. Thus the 2 year age difference!
I'm preparing to take the DAT in a few weeks and I like math. So it frustrates me when I get anything wrong haha. I have a lot of work to do still though but I like reading the advice on these forums and am hoping I can kick the DAT's butt.