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
To solve this problem, we can set up a system of equations based on the information given.
Let's say the number of cows is represented by 'c,' and the number of horses is represented by 'h.'
According to the statement, "a farmer has 3 times as many horses as cows," we can write the equation:
h = 3c (Equation 1)
Also, it says that "there are 34 more horses than cows," which can be expressed as:
h = c + 34 (Equation 2)
Now we have a system of equations (Equation 1 and Equation 2) that we can solve.
Substitute Equation 1 into Equation 2:
3c = c + 34
To isolate 'c,' we subtract 'c' from both sides of the equation:
3c - c = 34
Simplifying:
2c = 34
Divide both sides by 2:
c = 17
Now, substitute the value of 'c' back into Equation 1 to find 'h':
h = 3(17) = 51
Therefore, the farmer has 17 cows and 51 horses.