A fish and game warden captures and tags 66 deer in a local forest. A month later he captures 100 deer and finds that 17 of them are tagged. Estimate the actual number of deer in the forest.
A. 149
B. 1,022
C. 578
D. 389
We can use cross-multiplication to set up a proportion:
66/total number of deer = 17/100
Simplifying, we can write:
total number of deer = (66 x 100)/17
total number of deer = 388.24
Rounded to the nearest whole number, the estimated actual number of deer in the forest is 389, which is answer choice D.
To estimate the actual number of deer in the forest, we can use a proportion based on the ratio of tagged deer to total deer in the second capture.
The proportion can be set up as:
tagged deer / total deer = tagged deer in later capture / total deer in later capture
Let's denote the total number of deer in the forest as "x":
66 / x = 17 / 100
To solve for "x", we can cross-multiply and solve for "x":
66 * 100 = 17 * x
6600 = 17x
Dividing both sides of the equation by 17:
6600 / 17 = x
Approximately 387.06 ≈ x
Since we are estimating the number of deer, we can round this to the nearest whole number:
x ≈ 387
Therefore, the estimate for the actual number of deer in the forest is approximately 387.
The closest option to this estimate is D. 389.