Question

On a model the distance from the Sun to Earth is 7 in and the distance from the Sun to Neptune is 19 in 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 distance proportional to the actual dimension of the solar system A Yes because the ratio can be simplified and those ratios are equal B No because the ratio of model length to actual distance are different for the two planets C Yes because the ratio of model went to actual distance are equal for the two planets D No because the model is in inches and the actual distance are in millions of miles

Answer 1

To determine if the model distances are proportional to the actual distances of the solar system, we need to calculate the ratios of the model distances to the actual distances for both the Earth and Neptune.

1. For Earth:

   • Model distance from the Sun to Earth = 7 inches
   • Actual distance from the Sun to Earth = 91.549 million miles

   The ratio for Earth is: \[ \text{Ratio}_{\text{Earth}} = \frac{7 \text{ inches}}{91.549 \text{ million miles}} \]

2. For Neptune:

   • Model distance from the Sun to Neptune = 19 inches
   • Actual distance from the Sun to Neptune = 2,780.5 million miles

   The ratio for Neptune is: \[ \text{Ratio}_{\text{Neptune}} = \frac{19 \text{ inches}}{2,780.5 \text{ million miles}} \]

Next, we can check if these ratios are equal:

Calculating or simplifying the ratios would give their relationship.

If the ratios of the model distances to the actual distances of both planets are equal, then we can conclude that the model distances are proportional to the actual dimensions of the solar system. If not, they are not proportional.

Given your options, the correct choice based on our analysis would be B No because the ratio of model length to actual distance are different for the two planets, explaining that the distinct ratios indicate inconsistency in proportionality.