Question

oscar has a map of the campground where he is staying. the scale shows that 4 inches on the map represents an actual distance of 2 miles. oscars tent is at campsite 4a. what number can you multiply each length on the map by to find the actual distance? options: \\(\frac{1}{2}\\) what is the actual distance from oscars campsite to the beach? (input box) mi an error has occurred. please enter a number. (map image: campsite 4a to beach is 2\\(\frac{1}{2}\\) in. vertically, 4a to general store is 3 in. horizontally, scale 4 in. : 2 mi)

Explanation:

First Sub - Question (What number to multiply map length by)

Step1: Find the scale factor

The scale is 4 inches on the map represents 2 miles. To find the number to multiply each map length by to get actual distance, we calculate the ratio of actual distance to map distance. So, we divide the actual distance (2 miles) by the map distance (4 inches).
$\frac{2}{4}=\frac{1}{2}$

Step1: Identify the map distance to the beach

From the map, the distance from Oscar's campsite (4A) to the beach is $2\frac{1}{2}$ inches (or $\frac{5}{2}$ inches).

Step2: Multiply by the scale factor

We know the scale factor is $\frac{1}{2}$ miles per inch. So we multiply the map distance by the scale factor: $\frac{5}{2}\times\frac{1}{2}=\frac{5}{4} = 1\frac{1}{4}$? Wait, no, wait. Wait, the scale is 4 inches map = 2 miles actual. So per inch, actual distance is $\frac{2}{4}=0.5$ miles per inch. The distance to the beach is $2\frac{1}{2}$ inches. So $2\frac{1}{2}\times0.5=\frac{5}{2}\times\frac{1}{2}=\frac{5}{4}=1.25$? Wait, no, looking at the map, the vertical distance from 4A to the beach is $2\frac{1}{2}$ inches. Wait, let's re - check. The scale is 4 inches map = 2 miles actual, so 1 inch map = $\frac{2}{4}=0.5$ miles actual. So for a map distance of $d$ inches, actual distance is $d\times0.5$. The map distance to the beach is $2\frac{1}{2}$ inches. So $2\frac{1}{2}\times0.5=\frac{5}{2}\times\frac{1}{2}=\frac{5}{4}=1.25$? Wait, but maybe I misread the map. Wait, the problem says "the beach" – looking at the map, the top has a beach - like area, and the distance from 4A to the beach is $2\frac{1}{2}$ inches. So using the scale factor of $\frac{1}{2}$ miles per inch (since 4 inches map = 2 miles actual, so 1 inch map = 0.5 miles actual), we calculate: $2\frac{1}{2}\times\frac{1}{2}=\frac{5}{2}\times\frac{1}{2}=\frac{5}{4}=1.25$? Wait, no, wait, maybe the first sub - question's answer is $\frac{1}{2}$ (since 4 inches map = 2 miles actual, so multiplier is $\frac{2}{4}=\frac{1}{2}$ miles per inch). Then for the beach, the map distance is $2\frac{1}{2}$ inches. So actual distance is $2\frac{1}{2}\times\frac{1}{2}=\frac{5}{2}\times\frac{1}{2}=\frac{5}{4}=1.25$? Wait, but let's do it again. 4 inches map = 2 miles actual. So 1 inch map = $\frac{2}{4}=0.5$ miles actual. The distance from 4A to the beach is $2\frac{1}{2}$ inches. So $2.5\times0.5 = 1.25$ miles.

Answer:

$\frac{1}{2}$

Second Sub - Question (Actual distance to the beach)