Karl’s and eddie’s ages added together are equal to 65. 10 years ago, Karl was twice as old as Eddie. How old are they now

9514 1404 393

Step-by-step explanation:

10 years ago, the sum of their ages was 65 -2·10 = 45.

If Karl was twice as old as Eddie, his contribution was 2/3 of the sum and Eddie's was 1/3. That is, Karl was (2/3)(45) = 30 and Eddie was 15 at that time.

Now, Karl is 40 and Eddie is 25.

__

This can be solved using a system of equations.

  e = 65 -k

  (k -10) = 2(e -10)

Substituting the first equation into the second gives ...

  k -10 = 2((65 -k) -10)

  k -10 = 110 -2k . . . . . . . simplify

  3k = 120 . . . . . . . . . . . . add 10+2k

  k = 40

  e = 65 -40 = 25