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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">解：（</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span><span style="line-height:150%"><span style="font-family:新宋体">）设参加活动的教师有</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">a</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">人，学生有</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">b</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">人，依题意有：</span></span></span></span></span><br />
<img height="38" src="/uploads/meth/20211018/3b55a3287e9ae7a503f3c3f4a8ad1da5.png" width="108" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">解得</span></span></span></span></span><img height="38" src="/uploads/meth/20211018/330e7763893a6ecd59af4be459fe3e7d.png" width="44" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">故参加活动的教师有</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">10</span></span><span style="line-height:150%"><span style="font-family:新宋体">人，学生有</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">50</span></span><span style="line-height:150%"><span style="font-family:新宋体">人；</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">故答案为：</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">10</span></span><span style="line-height:150%"><span style="font-family:新宋体">；</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">50</span></span><span style="line-height:150%"><span style="font-family:新宋体">；</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">）</span></span><span style="line-height:150%">①</span><span style="line-height:150%"><span style="font-family:新宋体">依题意有：</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">y</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">56<i>x</i>+36</span></span><span style="line-height:150%"><span style="font-family:新宋体">（</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">10</span></span><span style="line-height:150%"><span style="font-family:新宋体">﹣</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">x</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">）</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">+30</span></span><span style="line-height:150%"><span style="font-family:新宋体">×</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">50</span></span><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">20<i>x</i>+1860</span></span><span style="line-height:150%"><span style="font-family:新宋体">．</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">故</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">y</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">关于</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">x</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">的函数关系式是</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">y</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＝</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">20<i>x</i>+1860</span></span><span style="line-height:150%"><span style="font-family:新宋体">（</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">0</span></span><span style="line-height:150%"><span style="font-family:新宋体">＜</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">x</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">＜</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">10</span></span><span style="line-height:150%"><span style="font-family:新宋体">）；</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%">②</span><span style="line-height:150%"><span style="font-family:新宋体">依题意有</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:"Times New Roman"">20<i>x</i>+1860</span></span><span style="line-height:150%"><span style="font-family:新宋体">≤</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">1910</span></span><span style="line-height:150%"><span style="font-family:新宋体">，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">解得</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">x</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">≤</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">2.5</span></span><span style="line-height:150%"><span style="font-family:新宋体">．</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">∵</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">x</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">为整数，</span></span></span></span></span><br />
<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">∴提早前往的教师最多只能</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">人．</span></span></span></span></span>

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