Question

review problems 4. a map of colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. are these two ways of reporting the scale the same? explain your reasoning.

Explanation:

Step1: Convert 20 miles to inches

Since 1 mile = 5280 feet and 1 foot = 12 inches, then 20 miles = 20×5280×12 inches.
20×5280×12 = 1267200 inches.

Step2: Compare the ratios

The first scale is 1 inch to 20 miles. In ratio - form, since 20 miles is 1267200 inches, the ratio is 1:1267200. The second ratio is 1:1267200.

Answer:

Yes, the two ways of reporting the scale are the same because when 20 miles is converted to inches (20×5280×12 = 1267200 inches), the ratio of 1 inch to 20 miles is equivalent to the ratio 1:1267200.