Let's represent the number of horses as x, the number of chickens as y, and the number of eggs as z. We are given:

The cost of a horse is 15 dollars, a chicken is 1 dollar, and an egg is 25 cents (0.25 dollars). You can spend up to 100 dollars. You want to buy a total of 100 items. We can represent these conditions as a system of linear equations:

15x + y + 0.25z = 100 (Total cost) x + y + z = 100 (Total items) We can solve this system of equations step by step:

Step 1: Solve the second equation for one of the variables, say z. z = 100 - x - y

Step 2: Substitute this expression for z in the first equation: 15x + y + 0.25(100 - x - y) = 100

Step 3: Simplify the equation and solve for y in terms of x. 15x + y + 25 - 0.25x - 0.25y = 100 14.75x + 0.75y = 75

y = (75 - 14.75x) / 0.75

Step 4: Find integer values for x and y that satisfy the equation. We'll loop through possible values of x and check if the corresponding value for y is an integer:

(Deleted some)

Now, we can calculate z using the value of x and y:

z = 100 - x - y = 100 - 0 - 100 = 0

So, you should purchase 0 horses, 100 chickens, and 0 eggs to reach a total of 100 items and spend exactly 100 dollars.