On a map of Alabama, one inch is equivalent to 100 miles. If the distance between two towns is 0.5 inches on the map, what is the actual distance between the towns?
A) 50 miles
B) 100 miles
C) 200 miles
D) 1000 miles
Please help! I'll mark Brainiest to the one who has the best explanation.

A

Step-by-step explanation:

The ratio is

1 inch : 100 miles

0.5 inch : X miles

1/100 = 0.5/X

X = 0.5 ÷ 1/100

X = 0.5 × 100/1

X = 50

Scale : 1in is 100 miles

If you look at it as a fraction, where the distances on the map equal the actual distances, you get this:

1/0.5 = 100/x

x is the unknown, because you don't know what 0.5 in is equal to. From here, you can cross-multiply to get x.

1 * x = 100 * 0.5

x = 50 (because 0.5 = 1/2 and half of 100 is 50)

Therefore, 0.5in = 50 miles in real life.

A simpler way to think about it is like this:

1in = 100 miles

0.5in = ?

To get 0.5in from 1in, you divide by 2. That means to get from 100 to the ?, you also divide by 2 because the two equations are proportional.

100/2 = 50.

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.