View source for 2005 CEMC Gauss (Grade 7) Problems/Problem 9

== Problem ==

A movie theatre has eleven rows of seats. The rows are numbered from <math>1</math> to <math>11</math>. Odd-numbered rows have <math>15</math> seats and even-numbered rows have <math>16</math> seats. How many seats are there in the theatre?

<math>\text{(A)}\ 176 \qquad \text{(B)}\ 186 \qquad \text{(C)}\ 165 \qquad \text{(D)}\ 170 \qquad \text{(E)}\ 171</math>

== Solution ==

There are six odd-numbered rows (rows <math>1, 3, 5, 7, 9, 11</math>).
These rows have <math>6\times 15 = 90</math> seats in total.
There are five even-numbered rows (rows <math>2, 4, 6, 8, 10</math>).
These rows have <math>5\times 16 = 80</math> seats in total.
Therefore, there are <math>90 + 80 = 170</math> seats in total in the theatre.  The answer is <math>D</math>.

==See Also==

{{CEMC box|year=2005|competition=Gauss (Grade 7)|before=8|num-a=10}}