Question

A map uses a scale of 1.25 inches = 60 miles.

a) Determine how many miles are represented by one inch.

b) If the distance between 2 cities on the map is 7 inches, how far apart are the cities in miles?

Answer 1

a. 48 miles are represented by one inch

b. The two cities are 336 miles apart

Explanation:

a.

The equations are directly proportional to each other, meaning we can equal them together

Set up the equation:

1.25 in/60 mi = 1 in/x mi

Variable x = number of miles represented by 1 inch

Cross multiply

1.25 × x = 60 × 1

1.25x = 60

Divide both sides by 1.25 to isolate the variable

1.25x ÷ 1.25 = 60 ÷ 1.25

1x = 48

x = 48

1 inch represents 48 miles

b.

We know 1 inch represents 48 miles, so to find how many miles 7 inches represents, we must multiply

Set up the equation:

7 inches × 48 miles

Solve:

7 × 48 = 336

7 inches represents 336 miles