Question

A farmer notes that in a field full of pigs and geese there are 32 heads and 94 feet how many of each animal are there

Answer 1

To solve this problem, we can set up a system of equations using the number of pigs and geese and the total number of heads and feet. By solving this system of equations, we find that there are 15 pigs and 17 geese in the field.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's let x represent the number of pigs and y represent the number of geese. From the problem, we know that:

• The total number of animals is 32: x + y = 32
• The total number of feet is 94: 4x + 2y = 94

We can solve this system of equations by substitution or elimination. Let's use the substitution method.

From the first equation, we can express x in terms of y as x = 32 - y. Substituting this into the second equation, we get:

4(32 - y) + 2y = 94

Simplifying, we have:

128 - 4y + 2y = 94

Combining like terms, we get:

-2y = -34

Dividing both sides by -2, we find that y = 17. Substituting this back into the first equation, we find that x = 15.

Therefore, there are 15 pigs and 17 geese in the field.

Answer 2

There are in total 17 geese and 15 pigs.

Step-by-step explanation:

Let us assume the number of geese = m

Also, the number of pigs = n

As, there are 32 heads.

⇒ m + n = 32 .... (1)

The number of legs each pig has = 4

So, the number of legs of n pigs = n ( Legs of 1 pig) = n (4) = 4 n

The number of legs each goose has = 2

So, the number of legs of m geese = n ( Legs of 1 goose) = m (2) = 2 m

As, there are total 94 feet.

⇒ 2 m + 4 n =94 .... (2)

Now, solving the given system for the value of m and n:

m + n = 32 ... (1) .......... x[ -2]

2 m + 4 n =94 ... (2)

Multiply (1) with -2 and add with (2),w e get:

-2 m - 2n + 2m + 4n = -64 + 94

⇒ 2n = 30

⇒ n = 30/2 =15

So, m = 32 - 15 = 17

Hence there are in total 17 geese and 15 pigs.