anonymous
  • anonymous
One day, a person went to horse racing area, Instead of counting the number of human and horses, he instead counted 74 heads and 196 legs. Yet he knew the number of humans and horses there. How did he do it, and how many humans and horses are there?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Let \[n_{human}\] be the number of humans and \[n_{horse}\]be the number of horses. You know that:\[n_{human}+n_{horse}=74\]since each species has only one head. For the number of legs,\[2n_{human}+4n_{horse}=196\]Using the first equation,\[n_{human}=74-n_{horse}\]and substituting this into the second,\[2(74-h_{horse})+4n_{horse}=196 \rightarrow 148+2n_{horse}=196\]so that\[n_{horse}=\frac{196-148}{2}=24\]Therefore, the number of humans is\[n_{human}=74-24=50\]

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