Question

in city lake, researchers caught, marked, and released 176 bass. later, they took a sample of 91 bass and found that 13 were marked. estimate the number of bass in the lake.
o 1232 bass
o 1183 bass
o 22 bass

Explanation:

Step1: Set up proportion

Let $x$ be the total number of bass in the lake. The proportion is $\frac{\text{number of marked bass in first - catch}}{\text{total number of bass in first - catch}}=\frac{\text{number of marked bass in second - catch}}{\text{total number of bass in second - catch}}$. We know that 176 bass were marked and released, and in the second sample of 91 bass, 13 were marked. So the proportion is $\frac{176}{x}=\frac{13}{91}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{176}{x}=\frac{13}{91}$ gives us $13x = 176\times91$.

Step3: Solve for $x$

First, calculate $176\times91=16016$. Then, $x=\frac{16016}{13}=1232$.

Answer:

1232 bass