Paula, dianna and annie are three friends. paula is twice as old as dianna, and in 2 years she will be three times as old as annie. if dianna is 5 years older than annie, how old is paula?

Make x = Paula, y = Dianna, and z = Annie

The 3 equations to set up and solve for are:

x = 2y

x + 2 = 3 (z + 2)

y = z + 5

Rewriting and reducing the equations as:

x = 2y = > y = x/2

x + 2 = 3 (z + 2) = > x + 2 = 3z + 6 = > x - 4 = 3z

y = z + 5

Then solving for x (Paula's age) gives:

x+2 = 3 (z-5+2) = 3 (x/2 - 3)

x+2 = 3/2 x - 9

x/2 = 11

x = 22