Xiao Ming counted the mathematics scores in the class, and the average score was 85.74. Later, he found that a classmate's original score was 97, and the statistics were mistakenly counted as 67. The average score after re-counting is 86.49. How many students are there in this class?
小明统计班里的数学成绩，平均分数为85.74，后来发现一个同学原来的分数为97，统计时误统计为67．重新统计后平均分数为86.49，此班共有多少个学生？
<gadget id="calculator">97 - 67</gadget>
<output>30</output>

<gadget id="calculator">86.49 - 85.74</gadget>
<output>0.75</output>

<gadget id="calculator">30 / 0.75</gadget>
<output>40</output>

<result>40</result>