Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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?

Sagot :

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.