The scale on a map shows that 5 centimeters = 2 kilometers. Part A What number of centimeters on the map represents an actual distance of 5 kilometers? Show y

Question

Rest of the question: The scale on a map shows that 5 centimeters = 2 kilometers.

Part A
What number of centimeters on the map represents an actual distance of 5 kilometers? Show your answer and explain your work.

Part B
What is the actual number of kilometers that is represented by 2 centimeters on the map? Show your answer and explain your work.

Answer 1

Both of these questions involve proportions. You can set up an equation using equivalent fractions. You want to express to ratio of cm to km in Part A. Given the scale factor 5 cm = 2 km, then we can let c = the number of cm that represent an actual distance of 5 km. The following equation can be formed:

 

5/2 = c/5

 

Both of these fractions are a ratio of cm to km. To solve, we can cross-multiply.

 

2c = 25

c = 12.5 cm 

 

You can use a similar process for Part B.