It takes 10 days for workshop A to complete a batch of parts. If workshop A and workshop B work together, it only takes 6 days to complete; if workshop B and workshop C work together, it takes 8 days to complete. Now the three workshops are working together. After completing the task, it is found that workshop A produced 2400 more parts than workshop B. How many parts did workshop C produce?
制作一批零件，甲车间要10天完成．如果甲车间与乙车间一起做，只要6天就能完成；乙车间与丙车间一起做，需要8天才能完成．现在三个车间一起做，完成任务后发现甲车间比乙车间多制作零件2400个，问丙车间制作了零件多少个？
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/6) - (1/10)</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(1/8) - (1/15)</gadget>
<output>7/120 = around 0.058333</output>

<gadget id="calculator">(1/6) + (7/120)</gadget>
<output>9/40 = around 0.225</output>

<gadget id="calculator">1 / (9/40)</gadget>
<output>40/9 = around 4.444444</output>

<gadget id="calculator">(1/10) * (40/9)</gadget>
<output>4/9 = around 0.444444</output>

<gadget id="calculator">(1/15) * (40/9)</gadget>
<output>8/27 = around 0.296296</output>

<gadget id="calculator">(4/9) - (8/27)</gadget>
<output>4/27 = around 0.148148</output>

<gadget id="calculator">2_400 / (4/27)</gadget>
<output>16_200</output>

<gadget id="calculator">(7/120) * (40/9)</gadget>
<output>7/27 = around 0.259259</output>

<gadget id="calculator">16_200 * (7/27)</gadget>
<output>4_200</output>

<result>4_200</result>