Question

HARD MATH QUESTION FOR MATH EXPERTS


A girl went to a horse race and she forgot to count the horses and humans there, but she knows there are 196 legs and 74 heads.

How many horses and humans were there at the horse race?

Answer 1

@Directrix @mathstudent55 @Hero

Answer 2

Well, you'd start with writing 2 equations that express what you know,

Answer 3

It's not a question for school or anything, i just wanted to put some minds to work, can you figure it out? :)

Answer 4

Let h = number of horses, and let p = number of people.
How many legs do h horses have?
How many legs do p people have?

Answer 5

4 h per horse 2 per human of course

Answer 6

h horses have 4h legs
p people have 2p legs

Answer 7

We know there are 196 legs in total, so
4h + 2p = 196

Answer 8

Where's the "hard" question?

Answer 9

there would be 24 horses and 50 humans.
@sw050399
Close.. keep trying

Answer 10

Since both horses and people have one head each, there are
h + p headds in total, but we know there are 74 heads, so we have
h + p = 74

Answer 11

I hardly consider this hard

Answer 12

I've seen far worse

Answer 13

Now you have two equations and two variables.
4h + 2p = 196
h + p = 74
Do you know how to solve a system of equations?

Answer 14

51 humans and 24 horses

Answer 15

How'd you figure it out so fast?

Answer 16

Girl would also be included

Answer 17

Troll.

Answer 18

exactly, thats where @sw050399 forgot to count. and @Hero Sorry, it took me a while to understand

Answer 19

So is your doubt clear now? :P

Answer 20

@mangnagelytis, not at all, I wanted to see if someone would understand this question as I.

Answer 21

\(2x + 4y = 196\)
\(x + y = 74\)
\(x + 3y = 122\)
y = 24

Thus x = 50 but +1 there as there is a girl also.

Answer 22

what about this one?

X 0 0 X

The figure above represents four offices that will be assigned randomly to four employees, one employee per office. If Karen and Tina are two of the four employees, what is the probability that each will be assigned an office indicated with an X?

a. 1/16
b. 1/12
c. 1/6
d. 1/4
e. 1/2

Answer 23

(I found this on a math practice website, supposedly "extremely hard."

Answer 24

This is how you solve the system of equations by elimination.
Multiply the second equation by -2 and write it below the first equation.
4h + 2p = 196
-2h - 2p = -148
----------------------(add the equations)
2h = 48
h = 24 (24 horses)
Now substitute 24 for h in the original second equation and solve for p:
h + p = 74
h + 24 = 74
h = 50 (50 people)

Answer 25

@mathstudent55 51 people is correct answer.

Answer 26

How many legs do 51 people have?

Answer 27

I was thinking the same @mathstudent55

Answer 28

50 people @ 2 legs per person = 100 legs
24 horses @ 4 legs per horse = 96 legs
-----------------------------------
74 heads 196 legs

Answer 29

You forgot to count, the girl
thats where you went wrong, but your systematic equations and work was very complete and thorough.

Answer 30

she didn't include herself when saying how many heads and legs she had counted while there.

Answer 31

@iloveyou1212 51 people + 24 horses have : 102 + 96 =198 legs..

Answer 32

The girl is included in the total count. She is a human, so she was counted with the humans.

Answer 33

Well not necessarily in the question, because technically she counted what was there, and when she made the final count, she didn't include herself.. That is what my teacher told me when we went over the answers..

Answer 34

@mathstudent55 You are correct, my teacher isn't bright.

Answer 35

My apologies:)

Answer 36

np

Answer 37

Someone took something from me. :)

Answer 38

great work @mathstudent55