to estimate the number of moths in a certain region, savannah traps 168 moths and marks them. she releases…

to estimate the number of moths in a certain region, savannah traps 168 moths and marks them. she releases these moths and then later catches 498, 28 of which are marked. to the nearest whole number, what is the best estimate for the moth population?

to estimate the number of moths in a certain region, savannah traps 168 moths and marks them. she releases these moths and then later catches 498, 28 of which are marked. to the nearest whole number, what is the best estimate for the moth population?

Answer

Explanation:

Step1: Set up proportion

Let $x$ be the total moth - population. The proportion is $\frac{\text{marked moths in first catch}}{\text{total population}}=\frac{\text{marked moths in second catch}}{\text{size of second catch}}$, so $\frac{168}{x}=\frac{28}{498}$.

Step2: Cross - multiply

Cross - multiplying gives us $28x = 168\times498$.

Step3: Solve for $x$

First, calculate $168\times498=168\times(500 - 2)=168\times500-168\times2=84000 - 336 = 83664$. Then $x=\frac{83664}{28}=2988$.

Answer:

2988