Question

There are 20 animals in the barn. Some are geese and some are buffalo. There are 64 legs in all. How many of each animal are there?

Answer 1

To solve the problem, we can set up a system of equations based on the given information and solve it to find the number of geese and buffalo.

Step-by-step explanation:

To solve this problem, we need to set up a system of equations based on the given information. Let's represent the number of geese as 'g' and the number of buffalo as 'b'. Since there are 20 animals in total, we can write the first equation as g + b = 20.

To find the number of legs, we need to consider that geese have 2 legs and buffaloes have 4 legs. So, the total number of legs can be expressed as 2g + 4b = 64.

We can now solve this system of equations to find the values of 'g' and 'b'. First, we can multiply the first equation by 2 to eliminate 'g': 2g + 2b = 40. Subtracting this equation from the second equation, we get: (2g + 4b) - (2g + 2b) = 64 - 40. Simplifying, we have 2b = 24. Therefore, b = 12.

Plugging this value back into the first equation, we have g + 12 = 20. Subtracting 12 from both sides, we find g = 8.

Therefore, there are 8 geese and 12 buffalo.

Answer 2

20 animals = x chickens (2 legs) + y horses (4 legs).

x+y=20 (total number of animals)

2x+4y=64 *total number of legs)

x+y=20

x+2y=32

If you solve this system of animal with 2 and 4 legs, you get 6 chickens and 14 horses

x=6

y=14

Try on your own!