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 18 - 2022 - Paper 2

Question 18

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 18 - 2022 - Paper 2

Step 1

Work out the proportion of tagged fish caught on Saturday

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Answer

To find the proportion of tagged fish, we divide the number of tagged fish by the total fish caught on Saturday:

$\text{Proportion of tagged fish} = \frac{45}{305}$

Calculating this gives approximately:

$\frac{45}{305} \approx 0.147$ .

Step 2

Use the proportion to estimate the total number of fish in the lake

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Answer

Let the total number of fish in the lake be ( x ). The number of tagged fish can also be expressed as:

$\frac{180}{x}$ .

Setting the proportions equal gives us:

$\frac{45}{305} = \frac{180}{x}$ .

Cross-multiplying leads to:

$45x = 180 \times 305$

Solving for ( x ):

$x = \frac{180 \times 305}{45} = 1220.$ .

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