The Scale On A Map Shows That 200 Miles Is Represented By 5 Inches On The Map. Which Proportion Can Be Used To Find The Distance On The Map, $x$, That Represents 50 Miles?A. $\frac{5}{200}=\frac{x}{50}$B.
Introduction
When working with maps, it's essential to understand the scale and proportions to accurately represent real-world distances. A map scale is a ratio that shows the relationship between the distance on the map and the actual distance in the real world. In this article, we'll explore how to use proportions to find the distance on a map that represents a given real-world distance.
Understanding the Map Scale
The problem states that 200 miles is represented by 5 inches on the map. This means that the map scale is 5 inches to 200 miles. To find the proportion, we need to set up a ratio that shows the relationship between the distance on the map and the actual distance in the real world.
Setting Up the Proportion
Let's use the information given in the problem to set up a proportion. We know that 200 miles is represented by 5 inches on the map. We can write this as a ratio:
5 inches : 200 miles
To find the proportion, we need to set up a ratio that shows the relationship between the distance on the map and the actual distance in the real world. We can do this by using the following proportion:
5 inches : 200 miles = x inches : 50 miles
Solving the Proportion
Now that we have the proportion set up, we can solve for x. To do this, we can cross-multiply and then divide both sides of the equation by the number of inches.
\frac{5}{200} = \frac{x}{50}
Cross-multiplying gives us:
5 \cdot 50 = 200 \cdot x
Simplifying the equation gives us:
250 = 200x
Dividing both sides of the equation by 200 gives us:
x = \frac{250}{200}
Simplifying the fraction gives us:
x = \frac{5}{4}
Conclusion
In conclusion, the proportion that can be used to find the distance on the map, x, that represents 50 miles is:
A.
This proportion can be used to find the distance on the map that represents a given real-world distance. By understanding the map scale and setting up the proportion correctly, we can accurately represent real-world distances on a map.
Discussion
The proportion can be used to find the distance on the map that represents 50 miles. This proportion is based on the map scale, which shows that 200 miles is represented by 5 inches on the map. By using this proportion, we can find the distance on the map that represents a given real-world distance.
Example Use Case
Suppose we want to find the distance on a map that represents 75 miles. We can use the proportion to find the distance on the map. Let's plug in the values and solve for x.
\frac{5}{200} = \frac{x}{50}
Cross-multiplying gives us:
5 \cdot 50 = 200 \cdot x
Simplifying the equation gives us:
250 = 200x
Dividing both sides of the equation by 200 gives us:
x = \frac{250}{200}
Simplifying the fraction gives us:
x = \frac{5}{4}
However, we want to find the distance on the map that represents 75 miles, not 50 miles. To do this, we can multiply the distance on the map that represents 50 miles by .
x = \frac{5}{4} \cdot \frac{75}{50}
Simplifying the equation gives us:
x = \frac{15}{8}
Therefore, the distance on the map that represents 75 miles is inches.
Conclusion
In conclusion, the proportion can be used to find the distance on the map that represents a given real-world distance. By understanding the map scale and setting up the proportion correctly, we can accurately represent real-world distances on a map.
Introduction
In our previous article, we explored how to use proportions to find the distance on a map that represents a given real-world distance. We discussed how to set up a proportion and solve for the distance on the map. In this article, we'll answer some common questions related to map scales and proportions.
Q&A
Q: What is a map scale?
A: A map scale is a ratio that shows the relationship between the distance on the map and the actual distance in the real world.
Q: How do I read a map scale?
A: To read a map scale, look for the ratio that shows the relationship between the distance on the map and the actual distance in the real world. For example, if the map scale is 1 inch : 100 miles, this means that 1 inch on the map represents 100 miles in the real world.
Q: How do I set up a proportion to find the distance on the map?
A: To set up a proportion, you need to know the map scale and the real-world distance you want to represent on the map. For example, if the map scale is 5 inches : 200 miles and you want to find the distance on the map that represents 50 miles, you can set up the proportion as follows:
5 inches : 200 miles = x inches : 50 miles
Q: How do I solve a proportion?
A: To solve a proportion, you can cross-multiply and then divide both sides of the equation by the number of inches. For example, if the proportion is:
5 inches : 200 miles = x inches : 50 miles
You can cross-multiply and then divide both sides of the equation by 200 to solve for x.
Q: What if I have a map scale that is not a simple ratio?
A: If you have a map scale that is not a simple ratio, you can still use proportions to find the distance on the map. For example, if the map scale is 1 inch : 100 miles, but the map is also scaled to show 1 inch : 500 feet, you can set up a proportion to find the distance on the map that represents a given real-world distance.
Q: Can I use proportions to find the distance on a map that represents a distance that is not a multiple of the map scale?
A: Yes, you can use proportions to find the distance on a map that represents a distance that is not a multiple of the map scale. For example, if the map scale is 1 inch : 100 miles and you want to find the distance on the map that represents 75 miles, you can set up a proportion and solve for x.
Q: How do I convert a map scale from one unit to another?
A: To convert a map scale from one unit to another, you can use proportions. For example, if the map scale is 1 inch : 100 miles and you want to convert it to feet, you can set up a proportion and solve for the new map scale.
Conclusion
In conclusion, understanding map scales and proportions is essential for accurately representing real-world distances on a map. By following the steps outlined in this article, you can set up a proportion and solve for the distance on the map that represents a given real-world distance.
Example Use Case
Suppose we want to find the distance on a map that represents 75 miles. We can use the proportion to find the distance on the map. Let's plug in the values and solve for x.
\frac{5}{200} = \frac{x}{50}
Cross-multiplying gives us:
5 \cdot 50 = 200 \cdot x
Simplifying the equation gives us:
250 = 200x
Dividing both sides of the equation by 200 gives us:
x = \frac{250}{200}
Simplifying the fraction gives us:
x = \frac{5}{4}
However, we want to find the distance on the map that represents 75 miles, not 50 miles. To do this, we can multiply the distance on the map that represents 50 miles by .
x = \frac{5}{4} \cdot \frac{75}{50}
Simplifying the equation gives us:
x = \frac{15}{8}
Therefore, the distance on the map that represents 75 miles is inches.
Conclusion
In conclusion, the proportion can be used to find the distance on the map that represents a given real-world distance. By understanding the map scale and setting up the proportion correctly, we can accurately represent real-world distances on a map.