A farmer went to your bank to ask for a loan. The bank agreed on offering $100 as long as the farmer would be able to buy exactly 100 animal

Very nice, happy7 !!!!!

Here's another way to solve this....we have more variables than equations, so we have infinite solutions....but only one makes sense... (as we shall see !!!)

Call the number of oxen, x, the number of pigs, y, and the number of sheep, z.

And we know that the total number of animals must = 100...so we have.....

x + y + z = 100     ...and solving for z, we have

z = 100 - x - y     (1)

And we know that each animal's value times their number summed together must = 100......so......

$10x + $3y + $.50z = 100

And replacing z with (1), we have

10x + 3y + .50(100 - x - y) = 100   ......simplify.......

10x + 3y + 50 - .50x - .50y = 100     .......simplify some more.....

9.5x + 2.5y  = 50     ........ multiply by 2 on each side......

19x + 5y  = 100

Now, notice that x must be some integer that is divisible by 5, because if we subtracted 19x from 100, this quantity would then be divisible by 5......i.e, making y an integer value, which is what we want..

And notice that x couldn't be any multiple of 5 larger than 5, because that would make y negative.....and we can't have a negative number of pigs!!!

So....x must be 5......so we have....

19(5) + 5y = 100

95 + 5y = 100     subtract 95 from both sides

5y = 5     divide both sides by 5

y = 1

And z = 100 - x - y .......so.......   z = 100 - 5 - 1  =  100 - 6   = 94

And just as Happy7  has said......we have 94 sheep, 1 p*g and 5 oxen.....

94 sheep, 1 p*g, and 5 oxes

That took me a while

94*.5=47.

1*3=3.

5*10=50.

94+1+5=100

47+3+50=100