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. oscar’s tent is at campsite 4a. what number can you multiply each length on the map by to find the actual distance? what is the actual distance from oscar’s campsite to the general store? (map includes segments like 3 in. from 4a to general store, scale 4 in. : 2 mi, and 2 1/2 in. segment)

Explanation:

Step1: Find the scale factor

The scale is 4 inches on the map represents 2 miles. So the scale factor (miles per inch) is $\frac{2}{4}=\frac{1}{2}$ mile per inch.

Step2: Determine the map distance

From the map, the distance from campsite 4A to the general store is 3 inches.

Step3: Calculate the actual distance

Multiply the map distance by the scale factor: $3\times\frac{1}{2}=\frac{3}{2} = 1.5$ miles. Wait, wait, no, wait the first part: Wait, the problem first asks "What number can you multiply each length on the map by to find the actual distance?" Let's re - address.

First, for the first sub - question: The scale is 4 inches (map) = 2 miles (actual). So to find the multiplier, we can find the ratio of actual to map. So $\frac{2\ miles}{4\ inches}=\frac{1}{2}\ miles\ per\ inch$. So the number is $\frac{1}{2}$.

For the second sub - question: The map distance from campsite to general store is 3 inches. Using the multiplier $\frac{1}{2}$ miles per inch, the actual distance is $3\times\frac{1}{2}=\frac{3}{2}=1.5$ miles? Wait, no, wait the scale: 4 inches = 2 miles, so 1 inch = $\frac{2}{4}=\frac{1}{2}$ mile. So 3 inches would be $3\times\frac{1}{2}=\frac{3}{2}$ miles? Wait, but maybe I misread the map. Wait the map shows the distance from 4A to General Store is 3 inches? Wait the image has "3 in." between 4A and General Store.

Wait, let's start over for the first part:

Part 1: Find the multiplier

Given that 4 inches on the map = 2 miles actual. So the multiplier (let's call it $k$) is such that actual distance = $k\times$ map distance. So $k=\frac{actual}{map}=\frac{2\ miles}{4\ inches}=\frac{1}{2}\ miles\ per\ inch$. So the number to multiply each map length by is $\frac{1}{2}$.

Part 2: Find actual distance from campsite to general store

The map distance (let's say $d_{map}$) is 3 inches. Using the formula actual distance $d_{actual}=k\times d_{map}$, with $k = \frac{1}{2}$ miles per inch and $d_{map}=3$ inches. So $d_{actual}=3\times\frac{1}{2}=\frac{3}{2}=1.5$ miles? Wait, but maybe the map distance is different? Wait the image shows "3 in." between 4A and General Store. So that's correct.

Wait, but maybe I made a mistake in the scale. Wait the problem says "4 inches on the map represents an actual distance of 2 miles". So 4 inches = 2 miles, so 1 inch = $\frac{2}{4}=0.5$ miles. So the multiplier is 0.5 (or $\frac{1}{2}$). Then for 3 inches, actual distance is $3\times0.5 = 1.5$ miles.

Answer:

• The number to multiply each map length by: $\frac{1}{2}$
• The actual distance from campsite to general store: $\frac{3}{2}$ miles (or 1.5 miles)