Question

two maps of a university campus are available to students. the scale from the campus to map a is 18 m to 6 cm. the scale from the campus to map b is 32 m to 8 cm. the distance from the cafeteria to the math building is 15.5 cm on map a. the distance from the bookstore to the math building is 12.5 cm on map b. which is closer to the math building, the cafeteria or the bookstore? choose one option from each drop - down menu to answer the question. the scale factor from map a to the campus is choose... the scale factor from map b to the campus is choose... the actual distance from the cafeteria to the math building using map a is choose... m. the actual distance from the bookstore to the math building using map b is choose... m. therefore, choose... is closer to the math building.

Explanation:

Step1: Calculate scale factor of map A

First, simplify the scale of map A. Given 18 m to 6 cm, convert 18 m to 1800 cm. The scale is 1800 cm to 6 cm. The scale factor from map A to the campus is $\frac{6}{1800}=\frac{1}{300}$.

Step2: Calculate scale factor of map B

For map B, 32 m = 3200 cm. The scale is 3200 cm to 8 cm. The scale factor from map B to the campus is $\frac{8}{3200}=\frac{1}{400}$.

Step3: Calculate actual distance from cafeteria to math building using map A

The distance on map A is 15.5 cm. Let the actual - distance be $x$. Using the scale factor $\frac{1}{300}=\frac{15.5}{x}$, then $x = 15.5\times300=4650$ cm = 46.5 m.

Step4: Calculate actual distance from bookstore to math building using map B

The distance on map B is 12.5 cm. Let the actual - distance be $y$. Using the scale factor $\frac{1}{400}=\frac{12.5}{y}$, then $y = 12.5\times400 = 5000$ cm = 50 m.

Answer:

The scale factor from map A to the campus is $\frac{1}{300}$. The scale factor from map B to the campus is $\frac{1}{400}$. The actual distance from the cafeteria to the math building using map A is 46.5 m. The actual distance from the bookstore to the math building using map B is 50 m. Therefore, the cafeteria is closer to the math building.