Whoever can figure this out is a freakin genius?

you have a $100 budget


you have to spend all 100. dont go over dont go under.


you have to buy 100 animals


The costs of the animals are:


chickens- 50 cents


cows-- 10 dollars


horses-3 dollars





you can buy any number of any animal. just make sure that you dont go over the $100 budget and dont buy more or less than 100 animals.Whoever can figure this out is a freakin genius?
This is the answer:





chickens- .50*94=$47


Buy 94 chickens, which costs $47 dollars.





cows- 10*5=$50


Buy 5 cows, which costs $50 dollars.





horses- 3*1=$3


Buy 1 horse, which costs $3 dollars.





$47+$50+$3= $100


94 chiochkens + 5 cows + 1 horse= 100 animalsWhoever can figure this out is a freakin genius?
Use a system of equations.


#of chickens = a


#of cows = b


#of horses = c





a + b + c = 100


0.5a + 10b + 3c = 100





a + 20b + 6c = 200


-(a + b + c = 100)


________________


19b + 5c = 100





Given that a, b, and c must be integers (you can't buy part of an animal), the two only possible answers are:


b = 5, c = 1


b = 0, c= 20





a + b + c = 100


a + 6 = 100 or a + 20 = 100


a = 94 or a = 80





94 chickens, 5 cows, and 1 horse = 100 animals


$47 + $50 + $3 = $100


or


80 chickens, 0 cows, and 20 horses = 100 animals


$40 + $0 + $60 = $100





Edit:


For most purposes, you do need 3 equations for 3 variables to get one solution. Since you know that your variables must be integers, you can narrow down your possible answers to two.
Let C be the numbers of chickens you buy, W the number of cows, and H the number of horses.





C + W + H = 100


0.5C + 10W + 3H = 100





Multiply the first equation by 10:


10C + 10W + 10H = 1000


Subtract the second equation from this:


(10C - 0.5C) + (10W - 10W) + (10H - 3H) = 1000 - 100


9.5C + 7H = 900


Multiply both sides by 2 to get rid of the decimal:


19C + 14H = 1800


Solve for C:


C = (1800 - 14H)/19


Let H = 1 (this is just one possibility)


Then:


C = 1786/19 = 94





C + W + H = 100


94 + W + 1 = 100


W = 5





Buy 94 chickens, 5 cows, and 1 horse
50 cents=$ 0,5





so





0,5x+10y+3z=$100 (divide all sides by 0,5)








x+20y+6z=200





so if you put x=94, y=5, z=1
20 horses @ $3 = $60


80 chickens @ $0.50 = $40


100 total animals, $100 total money spent