The students in the three classes of the sixth grade participate in extracurricular interest groups. The number of participants in the first class accounts for 1/4 of the total number of the sixth grade interest groups. The ratio of the number of participants in the second class to the number of the third class in the interest group is 4:5. The number of participants in class one is 84 less than the number of participants in class three. How many people in the sixth grade participate in the interest group?
六年级三个班的学生参加课外兴趣小组，一班参加的人数占六年级兴趣小组总人数的(1/4)，二班参加的人数与三班参加兴趣小组人数的比是4：5，一班参加的人数比三班参加的人数少84人，六年级共有多少人参加兴趣小组？
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">4 + 5</gadget>
<output>9</output>

<gadget id="calculator">5 / 9</gadget>
<output>5/9 = around 0.555556</output>

<gadget id="calculator">(3/4) * (5/9)</gadget>
<output>5/12 = around 0.416667</output>

<gadget id="calculator">(5/12) - (1/4)</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">84 / (1/6)</gadget>
<output>504</output>

<result>504</result>