The heights of 12 boys and 10 girls in a class are recorded. The average height of all 22 students in the class is $103 \mathrm{~cm}$. If the average height of the boys is $108 \mathrm{~cm}$, then the average height of the girls is
(A) $96 \mathrm{~cm}$
(B) $97 \mathrm{~cm}$
(C) $98 \mathrm{~cm}$
(D) $99 \mathrm{~cm}$
(E) $100 \mathrm{~cm}$

Part C: Each correct answer is worth 8.
Since the average height of all 22 students is $103 \mathrm{~cm}$, then the sum of the heights of all students in the class is $22 \times 103=2266 \mathrm{~cm}$.

Since the average height of the 12 boys in the class is $108 \mathrm{~cm}$, then the sum of the heights of all boys in the class is $12 \times 108=1296 \mathrm{~cm}$.

The sum of the heights of all the girls in class is the combined height of all students in the class less the height of all the boys in the class, or $2266-1296=970 \mathrm{~cm}$.

Since there are 10 girls in the class, their average height is $970 \div 10=97 \mathrm{~cm}$.

ANsWER: (B)