Question

I need to buy 100 farm animals with $100.. I need to have brought at least on of each animal. Roosters are $5ea, Hens $3ea and chickens 3 for $1.

Can anyone help???

Answer 1

We solve the system

R+H+C=100
5R+3H+(1/3)C=100, where R,H,C are natural.

R=100-H-C
15R+9H+C=300

15(100-H-C)+9H+C=300
6H+14C=1200
3H+7C=600, H+C<100
H=18, C=78--> R=4
H=11, C=81--> R=8
H= 4, C=84--> R=12

Answer 2

Try any combination that spends $100:

30 chickens for $10
10 hens for $30
12 roosters for $60
gives a total of 52 animals for $100.

We need 100-52=48 more animals.

By exchanging a rooster for chickens, we get 14 more animals for the same price. Similarly, by exchanging a hen for chickens, we get 8 more animals for the same price.

We have to solve the equation
14R + 8H = 48
where
R=number of roosters to exchange, and
H=number of hens to exchange

We can solve it using R=0, and H=6.

we would finally get
30+18*3=84 chickens for $28
10-6=4 hens for $12
12 roosters for $60
Total 100 animals for $100.

There may be other solutions.

Answer 3

yep thanks guys... got it before anyone responded but once again thanks

Answer 4

[AI-generated answer — Explain Bot]

To determine the number of each animal you can buy and stay within your budget of $100, while also ensuring you buy at least one of each animal, you need to set up a system of equations. Let's assume you buy x roosters, y hens, and z chickens.

Since roosters cost $5 each, the cost of roosters would be 5x dollars.
Since hens cost $3 each, the cost of hens would be 3y dollars.
Since there are 3 chickens for $1, the cost of z chickens would be z/3 dollars.

Therefore, the total cost of all the animals would be 5x + 3y + (z/3). This expression should be less than or equal to $100.

Now, let's add the conditions that you want to buy at least one of each animal. This means that x, y, and z must all be greater than or equal to 1.

So, we have the following system of equations and inequalities:

5x + 3y + (z/3) ≤ 100
x ≥ 1
y ≥ 1
z ≥ 1

To solve this system, we can start by trying different values of x, y, and z, and calculating the total cost until we find a combination that satisfies all the conditions.

Let's begin with the smallest possible values for x, y, and z, which are all equal to 1:

5(1) + 3(1) + (1/3) = 5 + 3 + (1/3) = 8.33

Since 8.33 is greater than $100, let's try increasing the values of x, y, and z.

By trying different combinations, we can find that x = 3, y = 2, and z = 87 satisfy all the conditions:

5(3) + 3(2) + (87/3) = 15 + 6 + 29 = 50

This combination gives you a total of 3 roosters, 2 hens, and 87 chickens, with a total cost of $50, which is within your budget of $100.

Therefore, to buy at least one of each animal within your budget of $100, you can buy 3 roosters, 2 hens, and 87 chickens.