Question

The distance between two points on a map is 8 centimeters/ The actual distance between the two locations is 112 miles. What is the scale of the map?

A)1 centi=8 miles
B)1 centi=12 miles
C)1 centi=14 miles
D)1 centi=23 miles

Answer 1

The question gives us the ratio 8cm : 112 miles. This ratio will still be equivalent if we divide both sides by the same number. So we divide both sides by 8 and get 8cm/8 : 112 miles / 8

Therefore, 1cm : 14 miles

Answer 2

To determine the scale of the map, we need to find out how many miles are represented by one centimeter on the map. We can do this by setting up a proportion:

8 centimeters / x = 112 miles / 1

Solving for x:

x = (8 centimeters x 1) / (112 miles)
x = 0.0714 centimeters/mile

So, one centimeter on the map represents 0.0714 miles. To make the scale easier to read, we can convert this to a more common unit, such as inches per mile:

1 centimeter = 0.3937 inches (approx.)
1 inch = 2.54 centimeters (exactly)

0.0714 miles x 63,360 inches/mile x 1/2.54 centimeters/inch = 1,415.748 inches/centimeter (approx.)

Therefore, the scale of the map is approximately:

1 centimeter = 1,415.748 inches/centimeter
1 inch = 1/1,415.748 centimeters
1 inch = 0.000706 mile

So, the answer is approximately:

D) 1 centi=23 miles