2005 CEMC Gauss (Grade 7) Problems/Problem 9

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Problem

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

$\text{(A)}\ 176 \qquad \text{(B)}\ 186 \qquad \text{(C)}\ 165 \qquad \text{(D)}\ 170 \qquad \text{(E)}\ 171$

Solution

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

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