As you can see, the goal of losing 20 pounds is not realistic or healthy. At 110 pounds, this woman still requires 100 pounds of lean body mass, but would only be carrying 10 pounds, or only 9% body fat. From the body fat chart above, you can see that this is a dangerously low percentage.
A better goal might be for the woman to reduce her body fat from 23% to 18%. In this case:
130 pounds x 0.18 = 23 pounds body fat.
100 pounds lean body mass + 23 pounds body fat = 123 pounds goal weight.
So, for this individual to achieve a lean, but healthy 18% fat, she would need to lose only 7 pounds of fat, reducing her weight from her current 130 pounds to 123 pounds. Losing more than 7 pounds means losing lean body mass(usually metabolically-active muscle tissue), which is clearly not desirable.
So before you decide that you need to "lose weight", remember to consider that "weight" consists of both lean body mass and body fat. Try to keep your weight loss goals realistic, and remember, keep the calorie-burning muscle, and lose only the fat.