Use this paragraph: A scale model of the solar system shows a dot placed at the center to represent the sun. Mercury is approximately 60,000,000 km from the sun and is placed on the model at a distance of 10 cm from the dot. Likewise, the Earth is approximately 150,000,000 km from the sun.

Question

At which distance from the dot should Earth be placed in the model?

(1 point)
Responses

25 cm
25 cm

4 cm
4 cm

900 cm
900 cm

21 cm
21 cm

Answer 1

To determine the correct distance for Earth in the scale model, we can set up a proportion based on the distances mentioned.

1. The distance of Mercury from the Sun in the model is 10 cm for 60,000,000 km:

   • This gives us a scale factor of \( \frac{10 \text{ cm}}{60,000,000 \text{ km}} \).

2. Now, we can find the distance for Earth, which is approximately 150,000,000 km:

   • Let \( d \) be the distance from the dot for Earth, then: \[ \frac{10 \text{ cm}}{60,000,000 \text{ km}} = \frac{d}{150,000,000 \text{ km}} \]

3. Cross-multiplying gives us: \[ 10 \text{ cm} \cdot 150,000,000 \text{ km} = d \cdot 60,000,000 \text{ km} \]

4. Solving for \( d \): \[ d = \frac{10 \text{ cm} \cdot 150,000,000 \text{ km}}{60,000,000 \text{ km}} \]

5. Simplifying this: \[ d = \frac{10 \cdot 150}{60} \text{ cm} \] \[ d = \frac{1500}{60} \text{ cm} \] \[ d = 25 \text{ cm} \]

Thus, the distance from the dot that Earth should be placed in the model is 25 cm.