Lets say the cost of her haircut is $x. This makes the cost of her perm 2x (twice as much). If lunch ($5), the perm ($2x) and the haircut ($x) cost, in total, $50, we can say:
50 = 5 + 2x + x
Combine like terms:
50 = 5 + 3x
Subtract 5 from both sides to isolate 3x
50 - 5 = 3x
45 = 3x
Divide all by 3 to isolate x
x = 45/3
x = 15
So the haircut is $15 and the perm is $30 (2*$15).