Due to the typist's resignation, a company has a backlog of the next batch of materials to be printed, and a fixed amount of materials to be printed is added every day. Assuming that the material is counted in pages, the typing speed of each typist is the same and fixed (the unit is minus/day). If the company employs 5 typists, all materials will be typed in 24 days; if the company employs 9 typists, all materials will be typed in 12 days. The company hired hard-working typists. After working for 8 days, due to the decrease in business, the newly added materials to be printed were reduced by half. As a result, these typists took 40 days to complete the typing work. Q: How many typists does the company employ?
由于打字员的辞职，一个公司积压下一批需要打印的材料，而且每天还要新增加固定数量需要打印的材料．假设材料以页计数，每个打字员的打字速度是相同的、固定的(单位是负/天)．如果公司聘任5名打字员，24天就恰好打完所有材料；如果公司聘任9名打字员，12天就恰好打完所有材料．公司聘任了苦干名打字员，工作8天之后，由于业务减少，每大新增的需要打印的材料少了一半，结果这些打字员共用40天才恰好完成打字工作．问：公司聘任了多少名打字员？
<gadget id="calculator">5 * 24</gadget>
<output>120</output>

<gadget id="calculator">9 * 12</gadget>
<output>108</output>

<gadget id="calculator">120 - 108</gadget>
<output>12</output>

<gadget id="calculator">24 - 12</gadget>
<output>12</output>

<gadget id="calculator">12 / 12</gadget>
<output>1</output>

<gadget id="calculator">24 * 1</gadget>
<output>24</output>

<gadget id="calculator">120 - 24</gadget>
<output>96</output>

<gadget id="calculator">1 * 8</gadget>
<output>8</output>

<gadget id="calculator">40 - 8</gadget>
<output>32</output>

<gadget id="calculator">12 / 12 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">32 * (1/2)</gadget>
<output>16</output>

<gadget id="calculator">96 + 8 + 16</gadget>
<output>120</output>

<gadget id="calculator">120 / 40</gadget>
<output>3</output>

<result>3</result>