In a model, the distance from the sun to Earth is 7 inches and the distance from the sun to Neptune is 19 inches. If the actual distance from the sun to Earth is 91.549 million miles and the actual distance from the sun to Neptune is 2,780.5 million miles, are the model’s distances proportional to the actual dimensions of the solar system?(1 point)

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Responses

Answer 1

To determine if the model's distances are proportional to the actual dimensions of the solar system, we can set up a proportion.

Let's define the scale factor (SF) as the ratio of the model distances to the actual distances.

For the distance from the sun to Earth:
SF = (Model distance from sun to Earth) / (Actual distance from sun to Earth)
SF = 7 inches / 91.549 million miles

For the distance from the sun to Neptune:
SF = (Model distance from sun to Neptune) / (Actual distance from sun to Neptune)
SF = 19 inches / 2780.5 million miles

To determine if the model's distances are proportional to the actual dimensions, we need to compare the scale factors. If the scale factors are equal, then the distances are proportional.

Comparing the two scale factors:
SF1/SF2 = (7 inches / 91.549 million miles) / (19 inches / 2780.5 million miles)
SF1/SF2 = (7 inches * 2780.5 million miles) / (19 inches * 91.549 million miles)

Simplifying the expression:
SF1/SF2 = (19553.5 inches * million miles) / (1721.831 million miles * inches)

The units cancel out:
SF1/SF2 = 19553.5 / 1721.831

Calculating the value:
SF1/SF2 ≈ 11.36

Since the scale factor ratio is not equal to 1, the model's distances are not proportional to the actual dimensions of the solar system.