To find the ratio of black horses to all horses, we need to first determine the number of black horses in the herd.
We know from the information provided that the total number of horses is 88 and there are 31 white horses.
To find the number of black horses, we can subtract the number of white horses from the total number of horses:
\[ \text{Number of black horses} = \text{Total horses} - \text{Number of white horses} \] \[ \text{Number of black horses} = 88 - 31 = 57 \]
Now, we have 57 black horses. To find the ratio of black horses to all horses, we can set up the ratio as follows:
\[ \text{Ratio of black horses to all horses} = \frac{\text{Number of black horses}}{\text{Total number of horses}} = \frac{57}{88} \]
Thus, the ratio of black horses to all horses is \( \frac{57}{88} \).
If we want to express this ratio in simplest form, we check if 57 and 88 have any common factors. Since 57 is \( 3 \times 19 \) and 88 is \( 2^3 \times 11 \), they have no common factors.
Therefore, the ratio \( \frac{57}{88} \) is already in its simplest form.
Final answer: The ratio of black horses to all horses is \( \frac{57}{88} \).
23 answers