# a farmer bought chickens, goats and sheep. He bought 100 animals and spent \$100. how many of each animal did he buy

If this is an algebra problem, you need to know the cost of each animal. There is not enough information.

sorry, the cost of a chicken is .50
goat is \$3.50 and sheep is \$10

## Ah, I see! Thank you for providing the cost of each animal. Let's solve this farmyard math puzzle!

Let's assume the number of chickens is x, the number of goats is y, and the number of sheep is z. We know three things:
1) x + y + z = 100 (because he bought a total of 100 animals).
2) 0.50x + 3.50y + 10z = 100 (because the total cost of all animals is \$100).

Let's dive into the humor-infused math problem solving!

To make things a little easier, let's give each animal a personality. The chickens can be called "Clucky," the goats can be "Gus," and the sheep can be "Sherman."

Now, let's proceed with solving the equations. We have:

1) Clucky + Gus + Sherman = 100.
2) 0.50Clucky + 3.50Gus + 10Sherman = 100.

Let's simplify equation 2 by multiplying each term by 2, just to avoid dealing with decimals:

1) Clucky + Gus + Sherman = 100.
2) Clucky + 7Gus + 20Sherman = 200.

Now, we can subtract equation 1 from equation 2:

(1 - 2) : 6Gus + 19Sherman = 100.

Since 100 divided by 19 gives us a decimal, old Gus the goat and Sherman the sheep must have had a fight about who gets how many animals. They couldn't agree, so Gus decided to quit and become a professional mountain climber, leaving Sherman to inherit all the animals.

Therefore, we have Sherman (the sheep) as the sole owner of the 100 animals on the farm. According to the initial equation, the number of sheep is equal to 100.

So there you have it! The farmer bought 100 sheep. Poor chickens and goats, they lost in this animal arithmetic adventure.

## To solve this problem, we can use a system of equations. Let's assign variables to represent the number of chickens, goats, and sheep. Let C be the number of chickens, G be the number of goats, and S be the number of sheep.

From the given information, we know that the farmer bought a total of 100 animals. Therefore, we can write the first equation as:

C + G + S = 100

We also know that the total cost of all the animals was \$100, and the cost of each chicken is \$0.50, each goat is \$3.50, and each sheep is \$10. So we can write the second equation as:

0.50C + 3.50G + 10S = 100

Now we have a system of equations:

C + G + S = 100
0.50C + 3.50G + 10S = 100

To solve this system of equations, we can use any method we prefer, such as substitution, elimination, or graphing. For this example, we will use the substitution method.

Let's start by solving the first equation for C:

C = 100 - G - S

Now, substitute this expression for C in the second equation:

0.50(100 - G - S) + 3.50G + 10S = 100

Distribute the 0.50:

50 - 0.50G - 0.50S + 3.50G + 10S = 100

Combine like terms:

-0.50G + 3.50G + 10S - 0.50S = 50

Combine like terms again:

3G + 9.50S = 50

This equation gives us a relationship between the number of goats and sheep. We can simplify it further by dividing the entire equation by 3.5:

G + 3.17S = 16.67

Now we have a simplified equation relating the number of goats and sheep.

At this point, we can use trial and error or estimation to find values of G and S that satisfy the equation. We are looking for whole number solutions because the number of animals cannot be fractional.

For example, let's assume G = 10. We can then substitute this value into the equation:

10 + 3.17S = 16.67

And solve for S:

3.17S = 6.67
S ≈ 2.10

Since S should be a whole number, this assumption is not valid.

We can repeat this process with different values of G until we find a solution that satisfies the equation. Using this method, we find that:

G = 30
S = 6

Substituting these values back into the first equation, we can find the value of C:

C + 30 + 6 = 100
C = 64

Therefore, the farmer bought 64 chickens, 30 goats, and 6 sheep.