Question

in a similar way to how you scaled the size of the planets, youll also scale the distances between each of the planets and the sun. the table contains the planets in our solar system and their average distances from the sun. to more easily compare these distances, youll scale them down using sheets of toilet paper. the ratio between earths distance from the sun and its scaled distance can be used to find the scaled distance for the other planets. earths distance of 149.6 million kilometers to the sun is scaled to 5.0 sheets of toilet paper as shown in the table. now lets find the scaled distance between mars and the sun as an example. using the calculations shown, marss distance to the sun of 227.9 million kilometers would be scaled to 7.6 sheets of toilet paper.
\\( \frac { 149.6 \text { million } \mathrm { km } } { 5.0 \text { sheets } } = \frac { 227.9 \text { million } \mathrm { km } } { d } \\)
\\( d \times 149.6 = 227.9 \times 5.0 \\)
\\( d = 7.6 \text { sheets } \\)
use this same process to complete the table with the scaled distances for the other planets. round each answer to the tenths place. if you need additional math help, visit the proportions section of the math review.

Explanation:

Step1: Set up proportion for Mercury

Let \(d_{Mercury}\) be the scaled distance for Mercury. The proportion is \(\frac{149.6}{5.0}=\frac{57.9}{d_{Mercury}}\). Cross - multiply: \(149.6\times d_{Mercury}=57.9\times5.0\).

Step2: Solve for \(d_{Mercury}\)

\(d_{Mercury}=\frac{57.9\times5.0}{149.6}=\frac{289.5}{149.6}\approx1.9\)

Step3: Set up proportion for Venus

Let \(d_{Venus}\) be the scaled distance for Venus. The proportion is \(\frac{149.6}{5.0}=\frac{108.2}{d_{Venus}}\). Cross - multiply: \(149.6\times d_{Venus}=108.2\times5.0\).

Step4: Solve for \(d_{Venus}\)

\(d_{Venus}=\frac{108.2\times5.0}{149.6}=\frac{541}{149.6}\approx3.6\)

Step5: Set up proportion for Jupiter

Let \(d_{Jupiter}\) be the scaled distance for Jupiter. The proportion is \(\frac{149.6}{5.0}=\frac{778.6}{d_{Jupiter}}\). Cross - multiply: \(149.6\times d_{Jupiter}=778.6\times5.0\).

Step6: Solve for \(d_{Jupiter}\)

\(d_{Jupiter}=\frac{778.6\times5.0}{149.6}=\frac{3893}{149.6}\approx26.0\)

Step7: Set up proportion for Saturn

Let \(d_{Saturn}\) be the scaled distance for Saturn. The proportion is \(\frac{149.6}{5.0}=\frac{1433.5}{d_{Saturn}}\). Cross - multiply: \(149.6\times d_{Saturn}=1433.5\times5.0\).

Step8: Solve for \(d_{Saturn}\)

\(d_{Saturn}=\frac{1433.5\times5.0}{149.6}=\frac{7167.5}{149.6}\approx47.9\)

Step9: Set up proportion for Uranus

Let \(d_{Uranus}\) be the scaled distance for Uranus. The proportion is \(\frac{149.6}{5.0}=\frac{2872.5}{d_{Uranus}}\). Cross - multiply: \(149.6\times d_{Uranus}=2872.5\times5.0\).

Step10: Solve for \(d_{Uranus}\)

\(d_{Uranus}=\frac{2872.5\times5.0}{149.6}=\frac{14362.5}{149.6}\approx96.0\)

Step11: Set up proportion for Neptune

Let \(d_{Neptune}\) be the scaled distance for Neptune. The proportion is \(\frac{149.6}{5.0}=\frac{4495.1}{d_{Neptune}}\). Cross - multiply: \(149.6\times d_{Neptune}=4495.1\times5.0\).

Step12: Solve for \(d_{Neptune}\)

\(d_{Neptune}=\frac{4495.1\times5.0}{149.6}=\frac{22475.5}{149.6}\approx150.3\)

Answer:

	Mercury	Venus	Earth	Mars	Jupiter	Saturn	Uranus	Neptune