Posted by **amanda** on Thursday, October 29, 2009 at 7:41pm.

Afarmer must purchase 100 animals. He must spend exactly $100. He must have at least one of each animals. Sheep cost $.50, cattle cost $1.00 and horses cost $10

- math -
**Reiny**, Thursday, October 29, 2009 at 7:57pm
First of all let me predict that there is no unique answer.

Here is why...

Let the number of horses be x

let the number of cattle by y

let the number of sheep be 100-x-y

then 10x + y + (1/2)(100-x-y) = 100

multiply 2 to get rid of fractions.

20x + 2y + 100 - x - y = 200

y = 100 - 19x

Of course we know that x and y must be natural numbers, (can't have 1/2 a cow)

so the largest value that x can have is 5

x=5, then y= 5 and 100-5-5 = 90

so 5 horses, 5 cattle and 90 sheep

let x = 4, y = 24, 100-4-24 = 72

so 4 horses, 24 cattle and 72 sheep

let x = 3, y = 43 100-3-43 = 54

3 horses, 43 cattle and 54 sheep

etc.

each of the above combinations will cost $100

(looks like this is from a book printed in the 1800's. Time for the schoolboard to upgrade)

## Answer this Question

## Related Questions

- math - You have exactly $100 to spend. You must get 100 animals. The chicks cost...
- math - I need to but exactly 100 farm animals I have $100. sheep cost $0.50, ...
- Math - I have $100.00 dollars to spend to buy 100 animals. Cows cost $50.00 each...
- math - You have exactly 100 dollars to buy 100 animals you must buy at least one...
- ALGEBRA 117 - 2. Biologists want to set up a station to test alligators in the ...
- math - a farmer bought chickens, goats and sheep. He bought 100 animals and ...
- math question corrected - a farmer bought chickens, goats and sheep. the cost of...
- Microeconomics - When average total cost is declining then: a) marginal cost ...
- Math 117 - 2. Biologists want to set up a station to test alligators in the lake...
- Algebra - 2. Biologists want to set up a station to test alligators in the lake ...