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2005 CEMC Gauss (Grade 7) Problems/Problem 9 - Revision history
2024-03-28T11:13:39Z
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2014-10-23T05:34:49Z
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2014-10-23T05:33:24Z
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RTG: /* See Also */
2014-10-22T22:57:52Z
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RTG: /* See Also */
2014-10-22T20:07:04Z
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RTG: /* Problem */
2014-10-22T19:58:03Z
<p><span dir="auto"><span class="autocomment">Problem</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>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?</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>A movie theatre has eleven rows of seats. The rows are numbered from <ins class="diffchange diffchange-inline"><math></ins>1<ins class="diffchange diffchange-inline"></math> </ins>to <ins class="diffchange diffchange-inline"><math></ins>11<ins class="diffchange diffchange-inline"></math></ins>. Odd-numbered rows have <ins class="diffchange diffchange-inline"><math></ins>15<ins class="diffchange diffchange-inline"></math> </ins>seats and even-numbered rows have <ins class="diffchange diffchange-inline"><math></ins>16<ins class="diffchange diffchange-inline"></math> </ins>seats. How many seats are there in the theatre?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>\text{(A)}\ 176 \qquad \text{(B)}\ 186 \qquad \text{(C)}\ 165 \qquad \text{(D)}\ 170 \qquad \text{(E)}\ 171</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>\text{(A)}\ 176 \qquad \text{(B)}\ 186 \qquad \text{(C)}\ 165 \qquad \text{(D)}\ 170 \qquad \text{(E)}\ 171</math></div></td></tr>
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https://artofproblemsolving.com/wiki/index.php?title=2005_CEMC_Gauss_(Grade_7)_Problems/Problem_9&diff=65473&oldid=prev
RTG: Created page with "== 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 ..."
2014-10-22T19:56:31Z
<p>Created page with "== 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 ..."</p>
<p><b>New page</b></p><div>== Problem ==<br />
<br />
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?<br />
<br />
<math>\text{(A)}\ 176 \qquad \text{(B)}\ 186 \qquad \text{(C)}\ 165 \qquad \text{(D)}\ 170 \qquad \text{(E)}\ 171</math><br />
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== Solution ==<br />
<br />
There are six odd-numbered rows (rows <math>1, 3, 5, 7, 9, 11</math>).<br />
These rows have <math>6\times 15 = 90</math> seats in total.<br />
There are five even-numbered rows (rows <math>2, 4, 6, 8, 10</math>).<br />
These rows have <math>5\times 16 = 80</math> seats in total.<br />
Therefore, there are <math>90 + 80 = 170</math> seats in total in the theatre. The answer is <math>D</math>.<br />
<br />
==See Also==<br />
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[[2005 CEMC Gauss (Grade 7)]]</div>
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