To find out how many barrels of corn the buffalo are fed each day, we first need to calculate how much corn is fed to the buffalo based on the amount fed to the elephants.
The elephants are fed \( 5 \frac{7}{10} \) barrels of corn each day. We can convert this mixed number into an improper fraction for easier calculation:
\[ 5 \frac{7}{10} = \frac{5 \times 10 + 7}{10} = \frac{50 + 7}{10} = \frac{57}{10} \]
Next, we know that the buffalo are fed \( \frac{3}{5} \) as much corn as the elephants. To find out how much that is, we multiply the corn fed to the elephants by \( \frac{3}{5} \):
\[ \text{Corn for buffalo} = \frac{3}{5} \times \frac{57}{10} \]
Now, we multiply the fractions:
\[ = \frac{3 \times 57}{5 \times 10} = \frac{171}{50} \]
Finally, we can convert this improper fraction back into a mixed number if needed:
To convert \( \frac{171}{50} \):
- Divide 171 by 50:
- 171 divided by 50 is 3 (since \( 3 \times 50 = 150 \))
- The remainder is \( 171 - 150 = 21 \)
Thus, \( \frac{171}{50} \) can be expressed as:
\[ 3 \frac{21}{50} \]
The buffalo are fed \( \frac{171}{50} \) barrels of corn each day, or as a mixed number:
\[ 3 \frac{21}{50} \text{ barrels} \]
So, the final answer is:
\[ \frac{171}{50} \text{ barrels} \quad \text{or} \quad 3 \frac{21}{50} \text{ barrels} \]
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