some researchers wanted to know how many smelt were living in a local lake, so they captured and tagged 410…

some researchers wanted to know how many smelt were living in a local lake, so they captured and tagged 410 smelt. later, the researchers trapped 720 smelt. of the smelt they trapped, 41 had tags. to the nearest whole number, what is the best estimate for the smelt population?
Answer
Explanation:
Step1: Set up proportion
Let $x$ be the total smelt population. The proportion is $\frac{\text{tagged smelt in first - catch}}{\text{total population}}=\frac{\text{tagged smelt in second - catch}}{\text{size of second - catch}}$, so $\frac{410}{x}=\frac{41}{720}$.
Step2: Cross - multiply
$41x = 410\times720$.
Step3: Solve for $x$
$x=\frac{410\times720}{41}$. Since $410\div41 = 10$, then $x = 10\times720=7200$.
Answer:
7200