you have to buy 100 animals. roosters cost 5.00, hens cost 1.00 and chicks cost .05cents. how many of each animal can I buy?
You left out the amount of money you have to spend.
sorry 100.00
You left out the cost of the purchases, typically $100.
Here is a similar version of this oldie.
If you had a $100.00 to spend and need to buy a 100 animals, and cows cost
$10.00, pigs $3.00, chichens .50 cents each,.how many of each can you buy?
Let C, P, and F be the numbers of cows, pigs, and fowl.
1--C + P + F = 100
2--10C + 3P + .5F = 100 or 100C + 30P + 5F = 1000
3--Multiplying (1) by 5 and subtracting from (2) yields 19C + 5P = 100
4--Dividing through by 5 gives P + 3C + 4C/5 = 20
5--4C/5 must be an integer as must be C/5
6--Let C/5 = k making C = 5k
7--Substituting (6) back into (3) gives 95k + 5P = 100 making P = 20 - 19k
8--k can only be 1 making C = 5, P = 1, and F = 94
Check: 10(5) + 3(1) + .5(94) = $100
Alternatively
Let C, P, and F be the numbers of cows, pigs, and fowl.
1--C + P + F = 100
2--10C + 3P + .5F = 100 or 100C + 30P + 5F = 1000
3--Multiplying (1) by 5 and subtracting from (2) yields 19C + 5P = 100
4--Solving for P, P = 20 - 19C/5
5--19C/5 must be an integer meaning that C must be evenly divisible by 5.
6--Thus, C must be 5 making P = 1, C = 5, and F = 94.
I'll let you work it out with your numbers.
please what is the answer
To determine how many of each animal you can buy, we need to set up a system of equations based on the given information. Let's denote the number of roosters as "r," the number of hens as "h," and the number of chicks as "c."
From the given information, we know:
1) The total number of animals bought should be 100. Therefore, the equation is:
r + h + c = 100
2) The cost of a rooster is $5.00, so the total cost of all roosters is 5r.
Similarly, the cost of a hen is $1.00, so the total cost of all hens is h.
The cost of a chick is $0.05, so the total cost of all chicks is 0.05c.
Therefore, the equation for the total cost is:
5r + h + 0.05c = Total Cost
We will solve this system of equations to find the values of r, h, and c.
To solve the equation, we need another equation to eliminate variables. Since the total number of animals is 100, we can solve for one variable and substitute it into the other equation.
From the first equation, we can rearrange it as follows:
r = 100 - h - c
Substituting this value of r into the second equation, we get:
5(100 - h - c) + h + 0.05c = Total Cost
Now, we can simplify and solve for h and c in terms of the total cost.
500 - 5h - 5c + h + 0.05c = Total Cost
500 - 4h - 4.95c = Total Cost
4h + 4.95c = 500 - Total Cost
From here, you can determine the values of h and c based on the total cost. The number of roosters (r) can then be calculated using the equation r = 100 - h - c.
For instance, if the total cost is $200, substitute it into the equation and solve for h and c.