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)

Answer 1

To determine whether the model's distances are proportional to the actual dimensions of the solar system, we can compare the ratios of the model's distances to the actual distances for both Earth and Neptune.

For Earth:
Model's distance = 7 inches
Actual distance = 91.549 million miles

Ratio = Model's distance / Actual distance = 7 inches / 91.549 million miles

For Neptune:
Model's distance = 19 inches
Actual distance = 2,780.5 million miles

Ratio = Model's distance / Actual distance = 19 inches / 2,780.5 million miles

To determine if the ratios are proportional, we need to compare the ratio for Earth to the ratio for Neptune:

Ratio for Earth / Ratio for Neptune = (7 inches / 91.549 million miles) / (19 inches / 2,780.5 million miles)

Simplifying, we get:

Ratio for Earth / Ratio for Neptune = (7 inches * 2,780.5 million miles) / (19 inches * 91.549 million miles)
= 194.5335 million inches miles / 1731.931 million inches miles
= 0.11222

Since the ratio of the model's distance to the actual distance is not equal for Earth and Neptune, the model's distances are not proportional to the actual dimensions of the solar system.