Lucy wants to find out the number of frogs in a pond near her house. She catches 54 of them, puts a leg band on each frog, and puts them back in the pond. The next week, she catches 70 frogs. Of the 70 frogs, 13 have a leg band. Based on this information, what is a reasonable estimate of the number of frogs in the pond?

Question

A) 208 B) 632 C) 291 D) 111

Answer 1

Let's use a proportion to estimate the total number of frogs in the pond:

$\frac{\text{number of banded frogs}}{\text{total number of frogs in first sample}}=\frac{\text{number of banded frogs in second sample}}{\text{total number of frogs in second sample}}$

Plugging in the given values, we get:

$\frac{54}{x}=\frac{13}{70}$

Cross-multiplying and solving for $x$, we get:

$x=\frac{54\times 70}{13}\approx 291$

So an estimate of 291 frogs in the pond is reasonable. Therefore, the answer is $\boxed{\textbf{(C) }291}$.

Answer 2

i do not understand can you put it in simple words bot

Answer 3

Sure! We can use a formula to help estimate the total number of frogs in the pond. We know that Lucy caught 54 frogs and put leg bands on all of them. Later, when she caught 70 more frogs, 13 of them already had leg bands. By comparing these numbers, we can figure out how many frogs must be in the pond overall.

We write out a formula using these numbers and solve it to get our estimate. Using this method, we estimate that there are around 291 frogs in the pond.