To solve for the missing number in the table, we need to examine the relationship between the distance on the map and the actual distance. Here is a step-by-step solution:
1. Identify the known distances:
- Distance on the map: 1 inch corresponds to 25 miles (actual distance).
- Distance on the map: 3 inches corresponds to 75 miles (actual distance).
2. Determine the scale factor:
- The scale factor is a consistent ratio between the distance on the map and the actual distance.
- Calculate the scale factor using the known points:
- For 1 inch on the map, the actual distance is 25 miles.
- Therefore, the scale factor = actual distance / distance on the map.
- Scale factor = 25 / 1 = 25.
- Confirm the scale factor using the other known point:
- For 3 inches on the map, the actual distance is 75 miles.
- Scale factor = 75 / 3 = 25.
We see that the scale factor is consistent and equal to 25.
3. Apply the scale factor to find the missing actual distance:
- Now, we will use the scale factor to find the actual distance that corresponds to 2 inches on the map.
- Actual distance = scale factor distance on the map.
- Actual distance = 25 2 = 50 miles.
4. Verify the solution:
- The missing actual distance for 2 inches on the map is 50 miles.
Given the above calculations, the missing number in the table is:
[tex]\[
\begin{tabular}{|l|c|c|c|}
\hline Distance on map (inches) & 1 & 2 & 3 \\
\hline Actual distance (miles) & 25 & 50 & 75 \\
\hline
\end{tabular}
\][/tex]
Therefore, the correct answer is [tex]\( \boxed{50} \)[/tex]. This corresponds to option B.
