The average age of a group of 140 people is 24 . If the average age of the males in the group is 21 and the average age of the females is 28 , how many females are in the group?
(A) 90
(B) 80
(C) 70
(D) 60
(E) 50
Let the number of females in the group be $F$.

Then since the average age of the females is 28 , then the sum of the ages of the females is $28 F$.

There are also $140-F$ males in the group, and the sum of there ages is $21(140-F)$.

So since the average of all of the ages is 24 , then

$$
\begin{aligned}
\frac{\text { Sum of all ages }}{140} & =24 \\
\frac{28 F+21(140-F)}{140} & =24 \\
28 F+21(140)-21 F & =24(140) \\
7 F & =3(140) \\
F & =60
\end{aligned}
$$

Therefore, there are 60 females in the group.

ANSWER: (D)