in six years rose will be two times as old as anne. Four years ago, anne was one third the age of rose. how old are they now

Rose is 34.

Anne is 14.

Step-by-step explanation:

Let rose be x years age now and anne be y years old now. Then:

x + 6 = 2 (y + 6)

x - 4 = 3 (y - 4)

Subtracting:

6 - - 4 = 2y + 12 - (3y - 12)

10 = - y + 24

-y = - 14

y = 14

Substituting for y:

x + 6 = 2 (14+6)

x = 40 - 6 = 34.