at the museum of natural history, there is a room filled with butterflies. patrons can come into the room…

at the museum of natural history, there is a room filled with butterflies. patrons can come into the room and watch the butterflies from close up. the butterfly caretaker, aubrey, decides to approximate the population of the butterflies. she uses a net to capture 22 butterflies, marks them, releases them, and then later catches 800 butterflies. of those 800 butterflies, 16 are marked. to the nearest whole number, what is the best estimate for the butterfly population?

at the museum of natural history, there is a room filled with butterflies. patrons can come into the room and watch the butterflies from close up. the butterfly caretaker, aubrey, decides to approximate the population of the butterflies. she uses a net to capture 22 butterflies, marks them, releases them, and then later catches 800 butterflies. of those 800 butterflies, 16 are marked. to the nearest whole number, what is the best estimate for the butterfly population?

Answer

Explanation:

Step1: Set up proportion

Let the total butterfly population be $x$. The proportion of marked butterflies in the first - catch to the total population is equal to the proportion of marked butterflies in the second - catch to the number of butterflies in the second - catch. So we have $\frac{22}{x}=\frac{16}{800}$.

Step2: Cross - multiply

Cross - multiplying gives us $16x = 22\times800$.

Step3: Calculate the right - hand side

$22\times800=17600$, so $16x = 17600$.

Step4: Solve for $x$

Dividing both sides by 16, we get $x=\frac{17600}{16}=1100$.

Answer:

1100