A farmer buys 100 live animals for $100. He buys chickens, goats, and sheep. How many of each does he buy if chickens cost $0.50 each, goats are $3.50 each, and sheep are $10 each?

Answer: The farmer bought 80 chickens, 16 goats, and 4 sheep in total.

Step-by-step explanation:

We're gonna call number of chicken: x, number of goats: y, and number of sheep: z.

So we know each chicken costs $0.50, so: 0.50x.

We also know that goats are $3.50 each, so: 3.50y.

Lastly, it is $10 per sheep. So, 10z.

Now, onto the equation:

0.50x + 3.50y + 10z = 100 (the total money paid)

We're gonna be using substitution.

But since we have three unknown variables, not two, we'll have to estimate (accurately) for one of the values in order to carry out the substitution.

After many tries, I got: there are 4 sheep. So now the equation would look something like this:

0.50x + 3.50y = 100 - 4.

Let's start solving.

But before we do so, we need another equation: y = 96 - x (since 100 - 4 = 96)

So now:

0.50x + 3.50 (96 - x) = 100 - 4

= 0.50x + 336 - 3.50x = 96

= 336 - 96 = 3.50x - 0.50x

= 240 = 3x

X = 240 divide by 3

X = 80.

Now we know the value of x (chicken.)

So we plug "x" into y = 96 - x

y = 96 - 80

y = 16 - how much goats purchased by farmer.

The answer: The farmer bought 80 chickens, 16 goats, and 4 sheep in total.