Sixth grade students participate in a math competition. It is known that each student can only participate in one kind of competition. The ratio of the number of people participating in the Hua Cup to the Hope Cup is 3:2, and the ratio of the number of people participating in the Innovation Cup to the Hope Cup is 5:4. More people participate in the Provincial Olympic Games than in the Hua Cup 4 people. Now 2 students who participated in the Hope Cup decided to participate in the Provincial Olympiad instead. May I ask how many people participated in the math competition?
六年级同学参加数学竞赛．已知每个同学只能参加一种比赛，参加华杯赛与希望杯人数的比是3：2，参加创新杯与希望杯人数的比是5：4，参加省奥赛的比参加华杯赛的多4人．现在有2个参加希望杯的同学决定改为参加省奥赛，此时省奥赛的人数正好是参加希望杯人数的2倍．请问一共有多少人参加了数学竞赛？
<gadget id="calculator">4 + 6</gadget>
<output>10</output>

<gadget id="calculator">8 - 6</gadget>
<output>2</output>

<gadget id="calculator">10 / 2</gadget>
<output>5</output>

<gadget id="calculator">4 * 5</gadget>
<output>20</output>

<gadget id="calculator">6 * 5</gadget>
<output>30</output>

<gadget id="calculator">5 * 5</gadget>
<output>25</output>

<gadget id="calculator">20 + 30 + 30 + 4 + 25</gadget>
<output>109</output>

<result>109</result>