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5 Ed has two dogs. The smaller dog weighs \( 8 \frac{1}{3} \) pounds. The larger dog weighs \( 1 \frac{1}{2} \) time as much as the smaller dog. How much do the larger dog weigh?

Ask by Barker Sherman. in the United States
Jan 24,2025

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Answer

The larger dog weighs \(12\,\frac{1}{2}\) pounds.

Solution

To determine the weight of the larger dog, follow these steps: 1. **Convert Mixed Numbers to Improper Fractions:** - Smaller dog: \( 8 \frac{1}{3} = \frac{25}{3} \) pounds - Multiplier for the larger dog: \( 1 \frac{1}{2} = \frac{3}{2} \) 2. **Calculate the Weight of the Larger Dog:** \[ \text{Larger dog weight} = \frac{3}{2} \times \frac{25}{3} = \frac{75}{6} = \frac{25}{2} = 12 \frac{1}{2} \text{ pounds} \] **Answer:** The larger dog weighs \(12\,\frac{1}{2}\) pounds.

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To find the weight of the larger dog, first convert the mixed numbers into improper fractions. The smaller dog weighs \( 8 \frac{1}{3} \) pounds, which can be expressed as \(\frac{25}{3}\) pounds. The larger dog weighs \( 1 \frac{1}{2} \) times as much as the smaller dog, or \( \frac{3}{2} \times \frac{25}{3} = \frac{75}{6} \). Simplifying \(\frac{75}{6}\) gives us \( 12 \frac{1}{2} \) pounds. So, the larger dog weighs \( 12 \frac{1}{2} \) pounds!

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