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One day, a person went to a horse racing area. Instead of counting the number of humans an horses, he counted 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

 Nov 15, 2017
 #1
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What in the heck are you talking about?! indecision

 Nov 15, 2017
 #2
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Use these equations to solve:

 

\(x+y=74 \tiny \text { Total heads; x = number of humans and y = number of horses} \\ 2x+4y=196 \tiny \text{ Total legs: each human has two and each horse has 4}\\ \text { Solve for x and y}\\ \)

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 Nov 15, 2017
 #3
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Solve the following system:
{x + y = 74 | (equation 1)
2 x + 4 y = 196 | (equation 2)

Swap equation 1 with equation 2:
{2 x + 4 y = 196 | (equation 1)
x + y = 74 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:
{2 x + 4 y = 196 | (equation 1)
0 x - y = -24 | (equation 2)

Divide equation 1 by 2:
{x + 2 y = 98 | (equation 1)
0 x - y = -24 | (equation 2)

Multiply equation 2 by -1:
{x + 2 y = 98 | (equation 1)
0 x+y = 24 | (equation 2)

Subtract 2 × (equation 2) from equation 1:
{x+0 y = 50 | (equation 1)
0 x+y = 24 | (equation 2)


x = 50 Humans     and          y=24 Horses
 

 Nov 16, 2017
edited by Guest  Nov 16, 2017

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