A farmer has 3 times as many horses as cows. if there are 34 more horses than cows, how many of each does he have?

Cows=x, horses=3x

3x-x=34=2x or x=17=no. of cows and horses are 17+34=51

51

Let's represent the number of cows as "x".

Since the farmer has 3 times as many horses as cows, we can represent the number of horses as "3x".

We are also given that there are 34 more horses than cows. So, we can set up the equation:

3x = x + 34

To solve this equation, we can subtract "x" from both sides:

2x = 34

Then, we divide both sides by 2 to solve for "x":

x = 34 / 2

Simplifying,

x = 17

So, the farmer has 17 cows.

Since he has 3 times as many horses as cows, he has:

3(17) = 51 horses.

Therefore, the farmer has 17 cows and 51 horses.

To solve this problem, let's set up some equations. Let's say the number of cows the farmer has is "c" and the number of horses is "h".

According to the problem, the farmer has 3 times as many horses as cows, so we can write the equation: h = 3c.

We also know that there are 34 more horses than cows, which can be written as: h = c + 34.

Now we have two equations with two variables. We can substitute the value of h from the second equation into the first equation to solve for c.

Substituting h = c + 34 into h = 3c, we get: c + 34 = 3c.

Now, we can solve this equation to find the value of c.

Subtracting c from both sides, we have: 34 = 2c.

Dividing both sides by 2, we get: c = 17.

So the farmer has 17 cows. Now we can substitute this value back into one of the original equations to find the number of horses.

Using the equation h = c + 34, we have: h = 17 + 34 = 51.

Therefore, the farmer has 17 cows and 51 horses.