Jim is making a diagram of the solar system. If he draws Neptune, which is 2795 million miles from the sun, 10 inches from the sun on his paper, how far away (to the nearest tenth of an inch) from the sun should he draw Mars, which is 142 million miles from the sun?
set up the ratio
x inches/142miles = 10 inches/2795miles
x = 10(142)/2795 inches
= .508
about 1/2 inch.
To determine the distance from the sun to draw Mars on Jim's paper, we can set up a proportion using the given distances.
We know that Neptune is 2795 million miles from the sun and is drawn 10 inches away on the paper. Let's call the distance from the sun to Mars on the paper "x inches."
The proportion can be set up as follows:
(neptune distance) / (neptune distance on paper) = (mars distance) / (mars distance on paper)
Substituting the given values:
2795 million miles / 10 inches = 142 million miles / x inches
Now, we can solve for "x inches" by cross-multiplying and then dividing:
(2795 million miles) * (x inches) = (10 inches) * (142 million miles)
(2795 million miles * x inches) = (10 inches * 142 million miles)
2795x = 1420 million
x = 1420 million / 2795
Calculating the value of 'x':
x ≈ 508.9566275 inches
Therefore, Jim should draw Mars approximately 508.9 inches away from the sun on his paper (to the nearest tenth of an inch).