How does she know how many heads and legs there are?
Algebra
Level
5
A girl went to a horse race and she forgot to count the horses and humans there, but she knows she saw there are 198 legs and 74 heads.
How many humans were there at the horse race?
Image credit: Wikipedia MichaelBueker
The answer is 51.
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Quite a tricky one if you forgot to count the girl.We have two different variables the humans and horses, so we can set up those equations Amount of legs 4 x + 2 y = 1 9 6 Amount of heads x + y = 7 4 solving those equations by substitution we get 4 x + 2 ( 7 4 − x ) = 1 9 6 thus it is 2 x + 1 4 8 = 1 9 6 solving this we get x=24 horse substituting into the second equation we get 2 4 + y = 7 4 , y = 5 0 then adding the girl gives 5 1 ( note the gives equations are horses have 4 legs and humans have 2 legs).