Question

Si una granja tiene chivos y canguros y hay 58 cabezas y 180 patas cuantos chivos y cuantos canguros hay en la granja

Answer 1

By setting up a system of equations with the data (58 heads and 180 legs) and solving for the number of goats and kangaroos, we determined that the farm has 32 goats and 26 kangaroos.

Step-by-step explanation:

Calculating the Number of Goats and Kangaroos

To find out how many goats (chivos) and kangaroos (canguros) there are on the farm, we can set up a system of equations based on the given information. There are 58 heads and 180 legs in total. Goats have 4 legs, and kangaroos have 2 legs.

We can set up the following equations where G represents the number of goats and K represents the number of kangaroos:

• 
  
• G + K = 58 (total heads)
• 
  
• 4G + 2K = 180 (total legs)

To solve this system, multiply the first equation by 2:

• 
  
• 2G + 2K = 116

Now subtract this new equation from the second one:

• 
  
• (4G + 2K) - (2G + 2K) = 180 - 116
• 
  
• 2G = 64
• 
  
• G = 32 (number of goats)

Plug this value into the first equation to find the number of kangaroos:

• 
  
• 32 + K = 58
• 
  
• K = 58 - 32
• 
  
• K = 26 (number of kangaroos)

Therefore, the farm has 32 goats and 26 kangaroos.

Answer 2

26 kangaroos on the farm
32 goats on the farm

Step-by-step explanation:

To find the number of goats and kangaroos on the farm, we need to determine the number of legs each animal has. Let's say that there are 'g' goats and 'k' kangaroos.

Since each goat has 4 legs, the total number of legs for all the goats is 4g. Similarly, since each kangaroo has 2 legs, the total number of legs for all the kangaroos is 2k.

Adding these two quantities, we have:

4g + 2k = 180

Since each goat has 1 head, the total number of heads for all the goats is g. Similarly, since each kangaroo has 1 head, the total number of heads for all the kangaroos is k.

Adding these two quantities, we have:

g + k = 58

Now, we have two equations and two unknowns. To solve for 'g' and 'k', we can use substitution or elimination method.

Let's use substitution method:

From the second equation, we can find g:

g = 58 - k

Substituting this in the first equation, we get:

4(58 - k) + 2k = 180

Expanding and solving, we get:

232 - 4k + 2k = 180

232 - 2k = 180

-2k = -52

k = 26

So, there are 26 kangaroos on the farm. To find the number of goats, we can use the first equation:

g = 58 - k = 58 - 26 = 32

Therefore, there are 32 goats on the farm.