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 beach? map includes campsites (4a, 4b, 4c, 4d, 4e, 4f), a camp area, a general store/beach area, with a 3-inch segment from 4a to the beach and a 2½-inch segment, plus a scale 4 in. : 2 mi

Explanation:

Part 1: Determine the multiplier

Step 1: Understand the scale

The scale is 4 inches on the map represents 2 miles in actual. So we need to find the miles per inch or the multiplier to convert map length to actual distance.
First, find the ratio of actual distance to map distance. The scale is 4 inches (map) = 2 miles (actual). So the multiplier (miles per inch) is calculated as $\frac{2\ \text{miles}}{4\ \text{inches}}=\frac{1}{2}\ \text{miles per inch}$? Wait, no, wait. Wait, 4 inches map = 2 miles actual. So to find how much 1 inch map represents, we do $2\div4 = 0.5$ miles per inch? Wait, no, wait the first question is "What number can you multiply each length on the map by to find the actual distance?". So the scale is 4 inches (map) = 2 miles (actual). So the conversion factor (multiplier) is $\frac{2\ \text{miles}}{4\ \text{inches}}=\frac{1}{2}\ \text{miles per inch}$? Wait, no, 2 miles for 4 inches, so per inch is $2/4 = 0.5$ miles per inch, which is $\frac{1}{2}$ miles per inch? Wait, no, 4 inches map = 2 miles actual, so the multiplier is (actual distance)/(map distance) = 2 miles / 4 inches = 0.5 miles per inch, which is $\frac{1}{2}$? Wait, no, 2 divided by 4 is 0.5, which is $\frac{1}{2}$? Wait, 2/4 simplifies to 1/2? Wait, no, 2 divided by 4 is 0.5, which is 1/2. Wait, but let's check: if the map length is, say, 4 inches, multiplying by 1/2 gives 2 miles, which matches the scale. So the multiplier is $\frac{1}{2}$? Wait, no, wait the scale is 4 inches (map) = 2 miles (actual). So the conversion factor is (actual distance) = (map distance) (2 miles / 4 inches) = (map distance) (0.5 miles per inch). So the multiplier is 0.5, which is $\frac{1}{2}$? Wait, no, 2 miles for 4 inches, so per inch is 2/4 = 0.5 miles. So the multiplier is 0.5, or $\frac{1}{2}$. Wait, but the problem says "What number can you multiply each length on the map by to find the actual distance?". So if the map length is in inches, multiplying by (2 miles / 4 inches) = 0.5 miles per inch. So the multiplier is 0.5, which is $\frac{1}{2}$. Wait, but let's confirm. Suppose the map length is 4 inches, 4 0.5 = 2 miles, which is correct. So the multiplier is $\frac{1}{2}$? Wait, no, 2 miles for 4 inches, so the ratio is 2/4 = 1/2. So the multiplier is 1/2. Wait, but maybe I got it reversed. Wait, scale is map : actual = 4 inches : 2 miles. So to get actual from map, we do (map length) (2 miles / 4 inches) = (map length) * 0.5 miles per inch. So the multiplier is 0.5, which is 1/2. So the answer for the first part is 1/2.

Step 2: Calculate the actual distance

Now, the distance from campsite 4A to the beach is 3 inches on the map (from the diagram: "3 in" between 4A and the beach). So we multiply the map length (3 inches) by the multiplier (1/2 miles per inch? Wait, no, wait earlier we had 4 inches map = 2 miles actual, so 1 inch map = 2/4 = 0.5 miles actual. So 3 inches map 0.5 miles per inch = 1.5 miles? Wait, no, wait 2 miles for 4 inches, so 1 inch is 0.5 miles, so 3 inches is 3 0.5 = 1.5 miles? Wait, but let's do it with the multiplier. The multiplier is (actual distance)/(map distance) = 2/4 = 1/2. So actual distance = map distance (2/4) = map distance 0.5. So for 3 inches, actual distance = 3 * 0.5 = 1.5 miles, which is 3/2 miles or 1.5 miles. Wait, but let's check the first part again. The first question: "What number can you multiply each length on the map by to find the actual distance?". The scale is 4 inches (map) = 2 miles (actual). So the conversion factor is 2 miles / 4 inches = 0.5 miles per inch. So the number to multiply is 0.5, which is 1/2. So that's t…

Answer:

(Part 1: Multiplier): $\frac{1}{2}$