Question

On the map below 1/4 inch represents one mile. Candler, Canton, and Oteen are three cities on the map. If Candler and Oteen are 3 1/2 inches apart on the map, what is the actual distance between Candler and Oteen in miles?

Answer 1

Answer:

14 miles

Step-by-step explanation:

Let "Candler" be known as "C" and "Oteen" as "O"

Given:

• 0.25 inch = 1 mile
• Distance between "C" and "O" (In inches): 3.5 inches

3.5 ------> 3.50

• ⇒ Distance between "C" and "O" (In inches): 3.50 inches

Comparing the rate (inches/mile) and the distance:

• ⇒ 0.25x = 3.50

Multiplying both sides by 100:

• ⇒ 25x = 350

Clearly, 350 is divisible by 25 as "50" is divisible by 25.

Divide both sides by 25 to isolate x:

• ⇒ 25x/25 = 350/25
• ⇒ x = 14

The actual distance between the two cities is 14 miles.

Answer 2

Answer:

14 miles

Step-by-step explanation:

Given:

• $\sf Scale=\dfrac14\:in : 1\:mile$

• distance between Candler and Oteen is 3 1/2 in

Let $x$ be the distance between Candler and Oteen in miles.

$\implies \dfrac14:1=3 \frac12:x$

$\implies \dfrac{\frac14}{1}=\dfrac{\frac72}{x}$

$\implies \dfrac14x=\dfrac72$

$\implies x=\dfrac72 \div \dfrac14$

$\implies x=\dfrac72 \times \dfrac41$

$\implies x=\dfrac{28}{2}$

$\implies x=14$