SOLUTION: For a research study, a biologist collected a sample of 203 plants, fish, and insects from a stream. There were 1/4 as many insects as there were fish in the sample. There were 1/5

Question 298355: For a research study, a biologist collected a sample of 203 plants, fish, and insects from a stream. There were 1/4 as many insects as there were fish in the sample. There were 1/5 as many plants as there were fish in the sample. How many fish were collected? A) 14 fish B)63 fish C)77 fish D)140 fish
Found 2 solutions by stanbon, kirti251:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
For a research study, a biologist collected a sample of 203 plants, fish, and insects from a stream.
Equations:
p + f + i = 203
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There were 1/4 as many insects as there were fish in the sample.
i = (1/4)f
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There were 1/5 as many plants as there were fish in the sample.
p = (1/5)f
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How many fish were collected?
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Substitute for i and p, then solve for "f".
(1/5)f + (1/4)f + f = 203
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Multiply thru by 20 to get:
4f + 5f + 20f = 4060
29f = 4060
---
# of fish = 140
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Cheers,
Stan H.

A) 14 fish B)63 fish C)77 fish D)140 fish

Answer by kirti251(6) (Show Source): You can put this solution on YOUR website!
Let the number of fish be x ,
number of plants be (1/5)x OR x/5
number of insects be (1/4)x OR x/4
Then,x + x/4 + x/5 = 203
Least Common Multiple (lcm) is 5 * 4 which is 20
x/1 * 20 + x/4 * 5 + x/5 * 4 =203
20x/20 + 4x/20 + 5x/20 =203
29x/20 =203
29x = 203 * 20=4060(on transporting 20 to the right side,the sign changes)
x = 4060/29=140(on transporting 29 to the right side multiplication changes to divison)
Therefore there are 140 fishes in the pond.
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