Question

lesson 19: rational equations and variation
lesson 19: rational equations and variation
score 60/100 answers: 10/17
question 12
environmentalists are trying to estimate the size of a fish population in a small lake.
using nets, they catch and tag 35 fish.
three months later, they catch 222 fish, and find that 26 of them are tagged.
assuming the amounts are proportional, estimate the number of fish in the lake.
round your answer to the nearest whole fish.
there are about fish in the lake.
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Explanation:

Step1: Set up the proportion

Let \(x\) be the total number of fish in the lake. The proportion is \(\frac{\text{tagged fish initially}}{\text{total fish}}=\frac{\text{tagged fish in second catch}}{\text{size of second catch}}\), so \(\frac{35}{x}=\frac{26}{222}\).

Step2: Cross - multiply

Cross - multiplying gives \(26x = 35\times222\).

Step3: Solve for \(x\)

First, calculate \(35\times222 = 7770\). Then \(x=\frac{7770}{26}\approx299\).

Answer:

299