Question 3 of 20
Sarah’s mother has a miniature village modeled after her home town. The model is 10 feet long and 7 feet wide. The actual village is 7 miles long. What is the village’s actual width? If necessary, round to the nearest tenth of a mile.
A. 4.9 miles
B. 10 miles
C. 1 mile
D. 0.7 mile
A.4.9
10/7 = 7/x
Cross multiply and solve for x.
To find the actual width of the village, we need to set up a proportion.
The model's width is 7 feet, which corresponds to the village's length of 7 miles.
Let's set up the proportion:
Model width / Model length = Actual width / Actual length
7 feet / 10 feet = Actual width / 7 miles
Now, let's solve for the actual width:
7 feet * 7 miles = 10 feet * Actual width
49 miles = 10 feet * Actual width
Actual width = 49 miles / 10 feet
Actual width ≈ 4.9 miles
Therefore, the village's actual width is approximately 4.9 miles.
Answer: A. 4.9 miles
To find the actual width of the village, we need to use the given information about the miniature village's dimensions.
The miniature village is modeled after Sarah's home town and has a length of 10 feet and a width of 7 feet. We are told that the actual length of the village is 7 miles.
To find the actual width of the village, we can set up a proportion using the ratios of the miniature village's dimensions to the actual village's dimensions. The ratio of the miniature village's length to its width is 10:7. We can set up the proportion:
10 feet / 7 feet = 7 miles / x
To solve for x, which represents the actual width of the village in miles, we cross-multiply:
10 feet * x = 7 feet * 7 miles
Now, we can solve for x by dividing both sides of the equation by 10 feet:
x = (7 feet * 7 miles) / 10 feet
Simplifying this expression, we get:
x = 49 miles * feet / 10 feet
The feet unit cancels out, and we are left with:
x = 49 miles / 10
Using a calculator:
x ≈ 4.9 miles
Therefore, the actual width of the village is approximately 4.9 miles.
So the correct answer is A. 4.9 miles.