Question
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Lucy bought \( \frac{28}{3} \) pounds of blueberries at the farmers' market, which she kept in 7 bags each holding an equal quantity. How many pounds of blueberries were in each bag?

Ask by Reeves Boyd. in the United States
Jan 24,2025

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Tutor-Verified Answer

Answer

Each bag contains \(\frac{4}{3}\) pounds of blueberries.

Solution

To determine how many pounds of blueberries are in each bag, follow these steps: 1. **Total Blueberries Purchased:** Lucy bought \(\frac{28}{3}\) pounds of blueberries. 2. **Number of Bags:** She divided the blueberries equally into 7 bags. 3. **Amount per Bag:** To find the amount in each bag, divide the total pounds by the number of bags: \[ \text{Amount per bag} = \frac{\frac{28}{3}}{7} \] 4. **Simplify the Division:** Dividing by a whole number is the same as multiplying by its reciprocal: \[ \frac{\frac{28}{3}}{7} = \frac{28}{3} \times \frac{1}{7} = \frac{28}{21} \] 5. **Reduce the Fraction:** Simplify \(\frac{28}{21}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 7: \[ \frac{28 \div 7}{21 \div 7} = \frac{4}{3} \] 6. **Final Answer:** Each bag contains \(\frac{4}{3}\) pounds of blueberries. This can also be expressed as: \[ 1 \frac{1}{3} \text{ pounds per bag} \] **Conclusion:** Each of the 7 bags contains \(\frac{4}{3}\) pounds (or \(1 \frac{1}{3}\) pounds) of blueberries.

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Beyond the Answer

To find out how many pounds of blueberries were in each bag, you need to divide the total pounds of blueberries by the number of bags. So, \( \frac{28}{3} \) pounds divided by 7 bags can be calculated as follows: \[ \frac{28}{3} \div 7 = \frac{28}{3} \times \frac{1}{7} = \frac{28 \times 1}{3 \times 7} = \frac{28}{21} \] Now simplify \( \frac{28}{21} \): \[ \frac{28 \div 7}{21 \div 7} = \frac{4}{3} \] Therefore, each bag contains \( \frac{4}{3} \) pounds of blueberries, which is equivalent to 1 pound and \( \frac{1}{3} \) pound or about 1.33 pounds.

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