Question

A teacher wants to build a scale model of the Earth and Pluto to compare their sizes. The Earth has a diameter of approximately 8000 miles and Pluto has a diameter of approximately 1500 miles. If the teacher builds a model of Earth with a diameter of 32 inches, what should be the diameter of her model of Pluto? Please explain the answer.
a) 5 1/3 inches
b) 6 inches
c) 6 3/2 inches
d) 8 inches

Answer 1

Answer:

B

Step-by-step explanation:

A scale model means that the ratios stay the same.

Therefore, Earth's diameter divided by Pluto's diameter is equal to the ratio of Earth's model's diameter divided by Pluto's model's diameter.

We can write this as

8000 / 1500 = 32/ Pluto's model's diameter. Representing Pluto's model's diameter as P, we can say

8000 / 1500 = 32 / P

multiply both sides by 1500 to remove a denominator

8000 = 32 * 1500 / P

multiply both sides by P to remove the other denominator

8000 * P = 32 * 1500

divide both sides by 8000 to isolate the P

P = 32 * 1500/8000

= 6 inches