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One day, a person went to a horse racing area. Instead of counting the number of humans an horses, he conuted 74 heads and 196 legs. How many humans and horses were there?
A.
37 humans and 98 horses
B.
24 horses and 50 humans
C.
31 horses and 74 humans
D.
24 humans and 50 horses



Answer :

thisisbenmanley
x = the number of humans and y = the number of horses.

x+y=74
2x+4y=196

Because the number of humans and horses together is 74, and the total number of legs (2 per every human, x, and 4 per every horse, y) is 196.  Then, just use elimination to solve.

[tex]-2(x+y=74)\\2x+4y=196\\\\-2x-2y=-148\\2x+4y=196\\\\2y=48\\y=24[/tex]

So, now that you have y, you can plug it into the first equation to find x:

[tex]x+y=74\\x+24=74\\x=50[/tex]

So, x = 50 and y = 24, so there are 50 humans and 24 horses.
The correct answer is B.

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