The mean (average) height of a group of children would be increased by $6 \mathrm{~cm}$ if 12 of the children in the group were each $8 \mathrm{~cm}$ taller. How many children are in the group?
(A) 16
(B) 14
(C) 21
(D) 26
(E) 9
The mean height of the group of children is equal to the sum of the heights of the children divided by the number of children in the group.

Therefore, the mean height of the group of children increases by $6 \mathrm{~cm}$ if the sum of the increases in the heights of the children, divided by the number of children in the group, is equal to 6 .

If 12 of the children were each $8 \mathrm{~cm}$ taller, then the sum of the increases in the heights of the children would be $12 \times 8=96 \mathrm{~cm}$.

Thus, 96 divided by the number of children in the group is equal to 6 .

Since $96 \div 16=6$, then the number of children in the group is 16 .

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