on a map the distance between two cities is 10 inches if 3/4 represents 30 miles how far is it between the two cities to the nearest mile

Question

A. 75

B. 225 miles

C. 300 miles

D. 400 miles

 

I dont understand how to solve this problem can someone thoroughly explain each step and why you have to do that so that I may understand please and thank you.

Answer 1

To start, let's call the answer we're looking for x.

 

This problem is about ratios. We know that the ratio of miles in real life to inches on the map is 30 miles for every 3/4 inches. We can represent that mathematically using a fraction: 30 miles / (3/4 inches).

 

This ratio is the same throughout the map, so if we know the number of inches is 10, we can find the number of miles x using an equation:

 

x / 10 = 30 / (3/4)

 

Now we can solve the equation:

 

x / 10 = 30 / .75

x / 10 = 40

x = 40 * 10

x = 400

 

10 inches on the map represents 400 miles in real life.

 

Explained a different way: 

We know that every 3/4 inch is 30 miles. Let's make that fact into miles per inch. 30 miles / (.75 inches) can be reduced to 40 miles per inch, since 30 divided by .75 is 40. Now we just take 40 miles per inch times 10 inches: 40 * 10 = 400. We get 400 miles.