SOLUTION: Charles is 23 years older than his sister carol. In 16 years he will be twice as old as carol. How old is each of them now?

Let H stands for Charles, C stands for Carol.

From the condition, you have these two equations:

H = C + 23,              (1)    ("Charles is 23 years older than his sister carol")

H + 16 =  2*(C+16).      (2)    ("In 16 years he will be twice as old as carol")


Substitute (1) into eq(2), replacing H. You will get a single equation for C:

(C+23) + 16 = 2*(C+16)  ====>

C + 39 = 2C + 32  ====>  39 - 32 = C  ====>  C = 7.


Answer.  Carol is 7 years old now.  Charles is 7+23 = 30 years old.