Question
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
Real Tutor Solution
Tutor-Verified Answer
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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Beyond the Answer
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!