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.

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

(1 point)
Responses

900 cm
900 cm

4 cm
4 cm

25 cm
25 cm

21 cm

1 answer

To determine the distance Earth should be placed from the dot in the scale model, we can set up a proportion based on the distances of Mercury and Earth from the Sun.

We know:

  • Mercury's real distance from the Sun: 60,000,000 km
  • Mercury's model distance from the Sun: 10 cm
  • Earth's real distance from the Sun: 150,000,000 km

We can set up a ratio to find Earth's model distance:

\[ \frac{\text{Distance of Earth}}{\text{Distance of Mercury}} = \frac{\text{Model distance of Earth}}{\text{Model distance of Mercury}} \]

Substituting the known values:

\[ \frac{150,000,000 \text{ km}}{60,000,000 \text{ km}} = \frac{x \text{ cm}}{10 \text{ cm}} \]

Calculating the left side:

\[ \frac{150,000,000}{60,000,000} = 2.5 \]

Now substituting back into the proportion:

\[ 2.5 = \frac{x}{10} \]

To find \(x\):

\[ x = 2.5 \times 10 = 25 \text{ cm} \]

So Earth should be placed at a distance of 25 cm from the dot in the model.

The correct answer is 25 cm.