Question

To determine the number of trout in a lake, a conservationist catches 79 trout, tags them, and throws them back into the lake. Later, 42 trout are caught, and 14 of them are tagged. How many trout would the conservationist expect to be in the lake?

A. 42
B. 79
C. 210
D. 150

Answer 1

None of the options are correct with the values given in the problem. The correct answer is 237 trout.

Step-by-step explanation:

1. Out of the 42 trout caught, 14 were tagged. To represent this, we can use the fraction
`(14)/(42)`.

2. The conservationist only tagged 79 fish, but we don't know how many trout are in the lake total. Mirroring the fraction in Step 1, we can create a fraction
`(79)/(x)` where x represents the total number of trout in the lake.

3. To find the expected number of trout in the lake, we put the fractions in Step 1 and Step 2 equal to one another and then solve for x.

• Set the fractions equal to each other:
  `(14)/(42)=(79)/(x)`
• Multiply both sides by x:
  `(14)/(42)x=79`
• Multiply both sides by 42:
  `14x=3318`
• Divide both sides by 14:
  `x=237`

4. The conservationist would expect there to be 237 trout in the lake.

Answer 2

Using the mark and recapture method, we can set up a proportion to estimate the population size. The calculation yields an estimated trout population of approximately 237, which is not one of the available options. There might be a rounding or transcription error in the question or answer choices.

Step-by-step explanation:

To determine the number of trout in the lake, the conservationist used a method known as mark and recapture. This method involves capturing a number of individuals from the population, marking them, and then releasing them back into their habitat. Later on, another sample is taken and the number of marked individuals within this second sample is counted. The ratio of the number of marked individuals in the second sample to the total number of individuals in the second sample is expected to be the same as the ratio of the number of marked individuals originally released to the total population.

Thus, if 79 trout are tagged and later 42 trout are caught with 14 of them being tagged, the conservationist can set up a proportion: 14 tagged in the second sample / 42 total in the second sample = 79 tagged initially / total population (N).

To find N, cross-multiply and solve for N: (14 / 42) = (79 / N)
14N = 79 x 42
N = (79 x 42) / 14
N = 237.

This value is not one of the available options, so it's possible we've made a calculation error. Let's check our math. After re-checking, we find that: (79 x 42) / 14 equals approximately 237, not one of the available options with choices A. 42, B. 79, C. 210, D. 150. The closest value to our calculation is 210 (Option C), which suggests that there might have been a rounding or transcription error in the question or the answer choices. The method used is correct, but there appears to be a discrepancy between the calculated result and the given options.