SOLUTION: A group of naturalists catch, tag and release 121 trout into a lake. The next day they catch 48 trout, of which 22 have been tagged. Using this ratio, how many trout would be est

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A group of naturalists catch, tag and release 121 trout into a lake. The next day they catch 48 trout, of which 22 have been tagged. Using this ratio, how many trout would be est      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 262976: A group of naturalists catch, tag and release 121 trout into a lake. The next day
they catch 48 trout, of which 22 have been tagged. Using this ratio, how many
trout would be estimated to be in the lake?
Answer by ajmisra(4) About Me  (Show Source):
You can put this solution on YOUR website!
Lets start the problem fromt he second part given about the next day:
If 22 trouts are already tagged from a bunch of 48 caught on any given day, the ratio of tagged/total would be 22/48 i.e 11/24 (on reduction of ratios i.e. dividing numerator and denominator by 2)
Apply this ratio to the total tagged 121 trouts out of say 'x' total trouts in the lake we could say,
121/x = 11/24 since we've assumed the tagged/total caught ratio on any given day is the same.
Solve this simply:
1) Cross multiply:
121 times 24 = 11 times x
ie. x = 121*24 / 11 = 11*24 (dividing by 11) = 264
Thus total estimated trouts in the lake is 264.