A4. On Mrs. Abraham's 50th birthday, she realized that she was as old as her three children combined. The daughter is 6 years older than the younger son, who is half as old as the older son. How old is the daughter?
(A) 9 years
(B) 13 years
(C) 17 years
(D) 23 years
(E) None of the above.
A4. Let the age of the older brother be denoted by $x$. Then the age of the younger brother is $\frac{x}{2}$, and the age of the daughter is $6+\frac{x}{2}$. Their total age is 50 years, so we have $50=x+\frac{x}{2}+6+\frac{x}{2}$. From this, it follows that $x=22$ years. The daughter is $6+\frac{x}{2}=17$ years old.