100 animals for $100?

Question

you have to buy 100 animals for $100

Rabbits are 8 for $1

cows are $10 each

goats are $1 each

10 points for the first correct answer

Answer 1

100 goats?

Answer 2

Let X = the number of rabbits

Let Y = the number of cows

Let Z = the number of goats.

From the problem you know the following relationships:

equation #1. X + Y + Z = 100 animals

equation #2. (X rabbits)($1/8rabbits) plus (Y cows)($10/1cow) plus (Z goats)($1/1goat) = $100 which when simplified reads:

(X/8)$ + (10Y)$ +(Z)$ = (100)$

Sorry, but this is a case of needing a 3rd equation, which relates the 3 unknowns to each other in a similar manner to the two I see in the problem. There is no mathematical solution for two equations in three unknowns. You need a 3rd relationship. To have a mathematical solution that you can solve and prove, you need as many equations as you have variables.

However, as was shown by another, the answer BY INSPECTION is, 72 rabbits, 7 cows and 21 goats, which when plugged into either of my equations does in fact solve the problem correctly, 100 animals for $100. I would like to see the work behind the other person's answer. There is other information, like X Y and Z are positive integers (parts of a cow don't count!) and X must be a multiple of 8 (parts of a dollar do not count!), which simply do not help solve the problem.

Now, if you added something like, "there are 3 times as many goats as cows", you would have equation #3: 3Z = Y. With the 3rd equation you can eliminate the variable Y by substitution in each of the other two, leaving 2 equations in 2 unknowns which CAN be mathematically solved for X and Z and then when substituted back into either of the 3 variable equations, solves for Y. Are you sure you included ALL of the information in your problem in this question?

Answer 3

its impossible. its a trick question.  

Answer 4

100 goats

DANGIT SHANE

Answer 5

Buy

72 Rabbits for $9 dollars

7 Cows for $70 dollars

21 Goats for $21 dollars

100 animals for $100 dollars

Answer 6

10 cows