If there are 80 head of cattle in the field and ratio dairy to beef is 1 3 How many there?

Let the number of dairy cows be \(x\). Then the number of beef cows is \(3x\). The total number of cows is \(x + 3x = 4x\). We know that the total number of cows is 80. So, we have the equation \(80 = 4x\). Dividing both sides of the equation by 4, we get \(20 = x\). Therefore, the number of dairy cows is 20.

Solution 2:

We can use a proportion to solve this problem. The ratio of dairy to beef cows is 1 to 3. This means that for every 1 dairy cow, there are 3 beef cows. The total number of cows is 80. So, we can set up the following proportion:

```

dairy/beef = 1/3

(dairy + beef)/beef = (1 + 3)/3

80/beef = 4/3

beef = 80/4 * 3

beef = 60

```

Therefore, the number of beef cows is 60. Since the ratio is 1 dairy cow to 3 beef cows, the number of dairy cows must be 60 / 3 = 20.