how do you solve proportion word problems

Question

San Jose and Madison are 6cm apart on a map that has a scale of 1cm:15km. How far apart are the real cities?

Answer 1

If 1cm on the map is 15km and the 2 cities are 6cm apart on the map all you need to do is

6 x 15km = 90km 

Answer 2

The key part to proportions is to remember that whatever the ratio they give you, the answer must have the same value.

In this case you know that there is 1cm of map for every 15km actual distance. You can write this as 1 centimeter per 15 kilometers: 1cm/15km

In order for the scale to be proportional every centimeter of map must correlate to 15 km of actual distance. This mean that for every 6 cm of map there is "x" km of actual distance.

So,

1 cm/15 km = 6 cm/x km

1cm*x km = 6 cm*15 km

x km = (90 cm*km)/1 cm = 90 km

Notice that it doesn't matter what quantity is on the top or bottom of the fraction as long as you make sure the other side uses the same ratio of units.

15km/1cm = x km/6cm

(6cm*15km)/1cm = 90 km