I have to buy 100 animals, I have to spend exactly 100 dollars, I have to get at least 1 of each. horses(X) = 10 bucks. cows(Y) = 1 buck. chickens(Z) = 50 cents
x+y+z = 100
so z = 100 - x - y
10 x + y + .5 z = 100
10 x + y + .5(100 - x - y) = 100
9.5 x + .5 y + 50 = 100
9.5 x + .5 y = 50
well x is 5 or less but must be even to avoid a half horse so try 4
4 horses is $40
so if we get 4 horses,
y + z = 96
y + .5 z = 60
--------------------
.5 z = 36
z = 72 then y = 24
==================
check
4 horses, 24 cows , 72 chickens
total 100 yes
4 * 10 + 24 * 1 + 72 * .5 = 40 + 24 + 36 = 100 check, whew !
please answer it
I'm kinda confused
Thank you so much
I really appreciate it
😃
You are welcome.
To tackle this problem, we can set up a system of equations to represent the given conditions:
Let X be the number of horses.
Let Y be the number of cows.
Let Z be the number of chickens.
Based on the given information, we have the following equations:
Equation 1: X + Y + Z = 100 (The total number of animals must be 100)
Equation 2: 10X + Y + 0.5Z = 100 (The total cost must be exactly 100 dollars)
We will now solve this system of equations to find the values of X, Y, and Z.
1. From Equation 1, we can express X in terms of Y and Z: X = 100 - Y - Z.
2. Substitute this value of X in Equation 2 to solve for Y and Z:
10(100 - Y - Z) + Y + 0.5Z = 100
1000 - 10Y - 10Z + Y + 0.5Z = 100
-9Y - 9.5Z = -900
3. Simplify and multiply both sides of the equation by -2/19 (to eliminate the coefficients):
Y + Z/2 = 100/19
4. Multiply through by 2 to eliminate fractions:
2Y + Z = 200/19
5. Now, we need to find integer solutions for Y and Z.
Since the cost of cows is lower than that of horses and chickens, it is logical to assign as many animals as possible to cows. So let's consider the maximum number of cows possible, which is 100.
Substitute Y = 100 into equation 5:
2(100) + Z = 200/19
200 + Z = 200/19
Z = 200/19 - 200
Z = 200 - (200/19)
Z = 200 - 10.5263158
Z ≈ 189.4736842
We obtained a non-integer value for Z, which means we cannot assign exactly 100 animals with a total cost of 100 dollars.
Given the constraints, it is not possible to purchase exactly 100 animals for exactly 100 dollars with at least one of each type of animal (horse, cow, and chicken).