Horses cost $10, pigs cost $3, and rabbits are only $0.50. a farmer buys 100 animals for $100, how many of each animal did he buy?

The correct answer to the following question is that there are 5 horses, 1 pig and 94 rabbits.

Explanation:

Given information -

Horses cost = $10

Pigs = $3

Rabbits = $.50

There are total of 100 animals, which are bought for $100 in total.

So by using simple equations we can solve this problem,

where let number of horses be x

number of pigs be y

number of rabbits be z

so the first equation that we can make by using given information is -

x + y + z = 100 (total of 100 animals bought )  _ _ equation 1

10 x + 3 y + .5 z = $100 _ _ equation 2

Now multiplying equation 2 by 2 and then subtract that from equation 1

(10 x + 3 y + .5 z = $100) x 2

= 20 x + 6 y + z = $200  _ _ equation 3

Now subtracting equation 3 from 1 -

20 x + 6 y + z = $200

          -

x + y + z = 100

19 x + 5 y = 100

Here 19 x and 5 y have to be a multiple of 5 ( where x and y are integers ), therefore the only possible value of x here can be 5 and if the value of x =5 , then the value of y will be equal to 1,

19 x 5 + 5 x 1 = 100

Now putting the value of x and y in equation 2,

10 x 5 + 3 x 1 + .5 x z = $100

50 + 3 + .5 z = 100

.5 z = 47 ( 100 - 53 )

z = 47 / .5

z = 94