Question

On a map of North Carolina, 27 centimeters represents 18 miles. Based on the map, what equation would calculate the number of miles between the two cities, y, when they measure x centimeters apart? Group of answer choices y = 2/3 x y = 3/2x y = 9x y = 18x

Answer 1

Let y represent number of miles between the two cities and x represent number of cm between both cities.

We have been given that on a map of North Carolina, 27 centimeters represents 18 miles. We are asked to determine the equation that would calculate the number of miles between the two cities, y, when they measure x centimeters apart.

We will use proportions to solve our given problem.

$\frac{\text{Number of miles between two cities}}{\text{Number of cm between two cities}}=\frac{18}{27}$

Upon substituting our given values in above equation, we will get:

$\frac{y}{x}=\frac{18}{27}$

$\frac{y}{x}=\frac{2}{3}$

Now we will multiply both sides by x.

$\frac{y}{x}\cdot x=\frac{2}{3}\cdot x$

$y=\frac{2}{3}\cdot x$

Therefore, our required equation would be $y=\frac{2}{3}\cdot x$ and 1st option is correct choice.