Subjects algebra

Hippo Mass 1Dd325

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1. **Stating the problem:** We have two hippos: a regular hippo with mass $25 \frac{1}{2}$ kg and a pygmy hippo. We want to understand which interpretation about their masses makes sense. 2. **Convert mixed numbers to improper fractions:** $25 \frac{1}{2} = 25 + \frac{1}{2} = \frac{50}{2} + \frac{1}{2} = \frac{51}{2}$ $5 \frac{3}{10} = 5 + \frac{3}{10} = \frac{50}{10} + \frac{3}{10} = \frac{53}{10}$ 3. **Kaipo's interpretation:** "25 1/2 ÷ 5 3/10 could represent the mass of the pygmy hippo if the regular hippo massed 5 3/10 times as much as the pygmy hippo." This means: $$\text{Regular mass} = 5 \frac{3}{10} \times \text{Pygmy mass}$$ So, $$\text{Pygmy mass} = \frac{\text{Regular mass}}{5 \frac{3}{10}} = \frac{\frac{51}{2}}{\frac{53}{10}}$$ 4. **Simplify Kaipo's expression:** $$\frac{\frac{51}{2}}{\frac{53}{10}} = \frac{51}{2} \times \frac{10}{53} = \frac{51 \times 10}{2 \times 53} = \frac{510}{106}$$ Simplify numerator and denominator by 2: $$\frac{\cancel{510}^{255}}{\cancel{106}^{53}} = \frac{255}{53} \approx 4.81 \text{ kg}$$ So, pygmy hippo mass is about 4.81 kg. 5. **Normani's interpretation:** "If the pygmy hippo massed 5 3/10 kg at birth, then the regular hippo massed 25 1/2 ÷ 5 3/10 times as much as the pygmy hippo." This means: $$\text{Regular mass} = \left(25 \frac{1}{2} \div 5 \frac{3}{10}\right) \times \text{Pygmy mass}$$ But this is inconsistent because $25 \frac{1}{2} \div 5 \frac{3}{10}$ is a number (about 4.81), so this would mean regular mass is 4.81 times pygmy mass, which contradicts the given data that regular hippo mass is $25 \frac{1}{2}$ kg. 6. **Conclusion:** Kaipo's interpretation correctly models the relationship: regular hippo mass is $5 \frac{3}{10}$ times the pygmy hippo mass, so dividing regular mass by $5 \frac{3}{10}$ gives pygmy mass. Normani's interpretation misuses the division and multiplication relationship. **Final answer:** Kaipo's only