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While walking in the country, you count 37 heads and 102 feet in a field of horses and geese. Howmany of each animal are there?

User KekuSemau
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1 Answer

19 votes
19 votes

In order to determine the number of horses and geeses, construct a system of equations, as follow:

There are 37 animals. If y is the number of horses and x the number of geeses, then, you can write:

x + y = 37

Now, consider that each geese has two feet and each horse has four feet. Due to you count 102 feet, then you can write:

2x + 4y = 102

Then, the system of equations is:

x+ y = 37

2x+ 4y = 102

Solve the previous system as follow:

Multiply the first equation by -2, then sum the result to the second equation and solve for y:

-2(x+ y = 37)

-2x - 2y = -74

-2x - 2y = -74

2x+ 4y = 102

2y = 28

y = 28/2

y = 14

Replace the previous value of y into any of the equations of the system and solve for x:

x + 14 = 37

x = 34 - 14

x = 20

Hence, there are 14 horses and 20 geeses.

User Himanshi Thakur
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