tourist group is going to order 80 pieces of certain commemorative medals priced at 100 yuan. The person in charge of the group said to the store manager: "If you are willing to reduce the price, then I will order 4 more pieces for every 1 yuan price reduction." It is 100 yuan more than the original one. How much is the cost of this commemorative badge?
某旅游团体准备订购定价为100元的某种纪念章80枚．团体负责人对商店经理说："如果你肯降价，那么每降价1元，我就多订购4枚．"商店经理算了一下，若降价5%，则由于旅游团体多订购，获得的利润反而比原来多100元，这种纪念章的成本是多少元？
<gadget id="calculator">80 * 100</gadget>
<output>8_000</output>

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">100 * (1/20) * 4 * 100</gadget>
<output>2_000</output>

<gadget id="calculator">80 * 100 * (1/20)</gadget>
<output>400</output>

<gadget id="calculator">100 * (1/20) * 4 * 100 * (1/20)</gadget>
<output>100</output>

<gadget id="calculator">2_000 - 8_000 - 400 - 100 - 100</gadget>
<output>-6_600</output>

<gadget id="calculator">8_000 + (-6_600)</gadget>
<output>1_400</output>

<gadget id="calculator">100 * (1/20) * 4</gadget>
<output>20</output>

<gadget id="calculator">20 - 80</gadget>
<output>-60</output>

<gadget id="calculator">80 + (-60)</gadget>
<output>20</output>

<gadget id="calculator">1_400 / 20</gadget>
<output>70</output>

<result>70</result>