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