- Identify total dog food as 10 pounds and consumption as 2/5 pounds per meal.
- Set up the division: \(10 \div \frac{2}{5}\).
- Multiply by the reciprocal to solve: \(10 \times \frac{5}{2} = 25\).
- Final answer is \(\boxed{25}\).
Explanation
- Analysis of the Problem
We need to determine how many meals 10 pounds of dog food will last, given that each meal consists of \(\frac{2}{5}\) pounds of food. We have a total supply of \(T = 10\) pounds and a consumption rate of \(M = \frac{2}{5}\) pounds per meal. To find the number of meals \(N\), we divide the total amount of food by the amount consumed per meal: \[N = \frac{T}{M}\] Substituting the given values, we get \[N = \frac{10}{\frac{2}{5}}\]
- Calculation and Conclusion
To perform the division by a fraction, we multiply by its reciprocal: \[N = 10 \times \frac{5}{2}\] We can simplify this expression by performing the multiplication: \[N = \frac{10 \times 5}{2} = \frac{50}{2} = 25\] Therefore, the food will last for 25 meals.
Examples
This type of problem is common in daily life when managing resources. For example, if you have a certain amount of ingredients for a recipe, knowing how much is used per serving allows you to calculate exactly how many servings you can prepare. This helps in meal planning, budgeting for groceries, and minimizing food waste by ensuring you only buy what is needed for the intended number of portions.