To determine how many meals Carmen can feed her dog with 28 pounds of dog food, we need to divide the total amount of food by the amount used per meal.
Carmen feeds her dog \( \frac{3}{8} \) pounds of dog food for each meal. We can set up the calculation as follows:
\[ \text{Number of meals} = \frac{\text{Total food}}{\text{Food per meal}} = \frac{28 \text{ pounds}}{\frac{3}{8} \text{ pounds per meal}} \]
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ \text{Number of meals} = 28 \times \frac{8}{3} \]
Now, we can simplify this calculation. First, convert 28 into a fraction:
\[ 28 = \frac{28}{1} \]
Now, multiply:
\[ \text{Number of meals} = \frac{28}{1} \times \frac{8}{3} = \frac{28 \times 8}{1 \times 3} = \frac{224}{3} \]
Now we can perform the division:
\[ \frac{224}{3} \approx 74.67 \]
Since Carmen cannot feed a fraction of a meal, we take the whole number part:
Carmen can feed her dog 74 meals with 28 pounds of dog food.
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