Question

Nine years ago, Katie was twice as old as Elena was then.

Elena realizes, "In four years, I'll be as old as Katie is now!"

Elena writes these equations to help her make sense of the situation:


`k-9=2(e-9)\\e+4=k`


If Elena is currently years old and Katie is years old, how old is Katie now?

Answer 1

Given that Elena is currently e years old and Katie is k years old. Now, nine years ago, Katie was twice as old as Elena was.

So, k - 9 = 2(e - 9)

⇒ k - 2e + 9 = 0 .............. (1)

And, in four years, Elena will be as old as Katie is now.

So, k = e + 4

⇒ k - e - 4 = 0 ............... (2)

Therefore, the equations (1) and (2) matches the conditions. (Answer)