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 those 70 frogs, 13 have a leg band. Based on this information, what is a reasonable estimate of the number of frogs in the pond?
A. 208
B. 632
C. 291
D. 111
Let x be the total number of frogs in the pond. We know that Lucy caught 54 of them and put leg bands on them, so the current number of leg-banded frogs is 54.
The next week, she caught 70 frogs and 13 of them had leg bands. This means that 13 out of (70 - 54) = 16 un-banded frogs were actually banded previously. So the total number of leg-banded frogs is now 54 + 13 = 67.
Since the ratio of leg-banded to un-banded frogs in the second catch is 13/16, we can set up the equation:
67/x = 13/16
Solving for x, we get:
x = (67 * 16)/13 = 208
Therefore, the reasonable estimate of the number of frogs in the pond is 208. The answer is A.