- Thread starter Osiris
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Hello. You also know that the numbers must be Whole numbers (from 1 through 9). In your attempts, did you try algebra? Did you guess and check?The [number for] each animal needs to be between 1-9 …

There isn't enough information given, to find all three numbers (directly) from solving equations. However, we could use algebra to find formulas for two of the unknowns -- each in terms of the remaining unknown. After that, we would use trial and error, to reason out the solution. Start by picking symbols for the unknown numbers.

Let B = the number of bats

Let C = the number of chickens

Let R = the number of rabbits

Choosing to find formulas in terms of B, for example, might yield something like this (made-up information):

C = 2B

R = B/2

If this were true (and it isn't), then we could see right away that B must be an even number.

From there, we would start guessing and checking -- trying B=2, B=4, B=6, etc. -- until we find Whole numbers for both C and R.

Please show your work, if you've tried anything. Check out the forum's submission guidelines, too. Cheers

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"five times the number of chickens I have plus three times the number of bats equals six times the number of rabbits": 5C+ 3B= 6R. We could also write that as 5C+ 3B- 6R= 0.

"The number of chickens plus twelve times the number of rabbits is equal to six times the number of bats I have": C+ 12R= 6B. We could also write that as C- 6B+ 12R= 0.

Seeing "3B" in one equation and "-6B" in the other I would multiply the first equation by 2 and add them: 10C+ 6B- 12R+ C- 6B+ 12R= 11C= 0 so C= 0. That contradicts the requirement that all the number be between 1 and 9. If that really is a requirement then there is no solution! I am going to assume that the solutions must be from 0 to 9.

With C= 0, the two equations reduce to 3B- 6R= 0 and -6B+ 12R= 0. Those both reduce to B= 2R.

With only two equations in 3 unknowns, we cannot find a single solution.

We can however, calculate all the solutions with all numbers from 0 to 9 by looking at possible values for R.

If R= 0 then B= 2(0)= 0 so one solution is that there are no animals at all!

If R= 1 then B= 2(1)= 2 so another solution is no chickens, 1 rabbit, and 2 bats.

If R= 2 then B= 2(2)= 4 so another solution is no chickens, 2 rabbits, and 4 bats.

If R= 3 then B= 2(3)= 6 so another solution is no chickens, 3 rabbits, and 6 bats.

If R= 4 then B= 2(4)= 8 so another solution is no chickens, 4 rabbits, and 8 bats.

If R is 5 or larger then B is larger than 9 so those are the only possible solutions.