A scientist samples of deer population and finds 200 deer in an area of 10 square miles. On average, how many deer can the scientist expect to find in an area of 300 square miles?
A: 20 deer
B: 60,000 deer
C: 320 deer
D: 6,000 deer
To solve this problem, we can set up a proportion.
We know that the number of deer is directly proportional to the area of land.
So, 200 deer / 10 square miles = x deer / 300 square miles, where x is the number of deer in the larger area.
Cross multiplying, we get 200 * 300 = 10 * x
Simplifying, we get 60000 = 10 * x
Dividing both sides by 10, we get x = 6000.
Therefore, the scientist can expect to find 6000 deer in an area of 300 square miles.
The correct answer is option D: 6,000 deer.
To solve this problem, we can use the concept of proportion.
Given:
Area 1 = 10 square miles
Number of deer in area 1 = 200 deer
We need to find:
Number of deer in area 2 when the area is 300 square miles.
Let's set up a proportion:
(area 1) / (area 2) = (number of deer in area 1) / (number of deer in area 2)
Plugging in the values we know:
(10 sq. miles) / (300 sq. miles) = (200 deer) / (number of deer in area 2)
To isolate the number of deer in area 2, we can cross-multiply and solve for it:
(10 sq. miles) * (number of deer in area 2) = (200 deer) * (300 sq. miles)
10 * (number of deer in area 2) = 60,000 deer
Dividing both sides by 10:
(number of deer in area 2) = 6,000 deer
Therefore, the scientist can expect to find 6,000 deer in an area of 300 square miles.
The correct answer is:
D: 6,000 deer
To determine the average number of deer in an area of 300 square miles, we can use the concept of proportionality.
First, we need to find the density of the deer population in the original area of 10 square miles. We divide the number of deer (200) by the area (10 square miles):
Density = Number of deer / Area = 200 deer / 10 square miles = 20 deer per square mile.
Now we can use this density to estimate the number of deer in the larger area of 300 square miles. We multiply the density (20 deer per square mile) by the area (300 square miles):
Number of deer = Density × Area = 20 deer per square mile × 300 square miles = 6,000 deer.
Therefore, the scientist can expect to find approximately 6,000 deer in an area of 300 square miles. Therefore, the correct answer is (D) 6,000 deer.