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