Question

Ratios and proportions. A ranger wants to estimate the number of antelope in a preserve. He catches 58 antelope, tags their ears, and returns them. Some time later, he catches 29 antelope and discovers that 7 of them are tagged. Estimate the number of antelope in the preserve.

Answer 1

a/b = c/d

Answer 2

can someone check this please...
I took x/58 = 7/29
29x = 406
x = 14
58 + 14 = 72
roughly 72 antelope in the preserve????

Answer 3

your variable x relates to the estimated total antelope in the preserve. Since he caught and tagged 58 out of x, I think you'll want to switch your left hand equation to 58/x instead of x/58. Then you have
58/x : 7/29

Answer 4

7 into 1682 = 240.285....

Answer 5

I put 58 on the bottom and 29 on the bottom to match those were caught

Answer 6

I added 14 to 58 because its the difference from those caught and tagged

Answer 7

Yes, but the fact that they are caught is not the association that you want for this ratio.

He originally caught 58 of an undetermined number = ratio1.
He then catches 29, of which 7 are tagged = ratio2.

The reason you want the x paired with the 29 is that the 29 represents a sample set with which you want to estimate the total population.

Answer 8

how do I answer the question of : estimate the number of antelope in the preserve... with that ratio? or solve it?

Answer 9

Okay. So we have our ratio of

58 7
-- : --
x 29

which can be read as 58 is to 7 as x is to 29.

You calculated the number above, by multiplying the top on one side by the bottom on the other: 58*29 = 1682 and then dividing by 7 = 240.285. So the estimate would be 240 antelope.

Answer 10

makes sense... thank you