Saffron wants to work out an estimate for the total number of fish in a lake. On Friday, Saffron catches 180 fish from the lake. She puts a tag on each of these fish and puts them back into the lake. On Saturday, Saffron catches 305 fish from the same lake. She finds that 45 of the 305 fish are tagged. Work out an estimate for the total number of fish in the lake.

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Saffron wants to work out an estimate for the total number of fish in a lake - Edexcel - GCSE Maths - Question 15 - 2022 - Paper 2

Question 15

Saffron wants to work out an estimate for the total number of fish in a lake. On Friday, Saffron catches 180 fish from the lake. She puts a tag on each of these fis... show full transcript

Worked Solution & Example Answer:Saffron wants to work out an estimate for the total number of fish in a lake - Edexcel - GCSE Maths - Question 15 - 2022 - Paper 2

Step 1

Calculate the proportion of tagged fish

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Answer

The number of tagged fish caught on Saturday is 45 out of a total of 305 fish caught. The proportion of tagged fish is calculated as follows:

ext{Proportion} = \frac{45}{305}

Step 2

Estimate the total number of fish in the lake

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Answer

Using the proportion of tagged fish, we can estimate the total fish population in the lake. If 180 fish were tagged on Friday, we set up the equation:

\text{Estimated total} = \frac{180}{\frac{45}{305}} = 180 \times \frac{305}{45}

Calculating this gives:

\text{Estimated total} = \frac{180 \times 305}{45} \approx 1220

Thus, the estimated total number of fish in the lake is approximately 1220.

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