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There were 5/8 as many shells as fish in an aquarium. After 50 shells and 8 fish were removed, the ratio of the number of shells to the number of fish became 1:4. Find the number of shells in the aquarium in the end.

 Oct 22, 2023
 #1
avatar+36919 
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f = fish #

5/8 f = shell number 

 

(5/8f -50) / (f-8)   = 1/4        <====  solve for f ....cross multiply to get:

  4 ( 5/8f-50) = f-8 

20/8f - 200 = f-8 

12/8 f = 192 

f = 128 

 

then ORIGINAL shells were   5/8 (128) = 80 

   FINAL shells = 80 - 50 = 30 shells in the end 

 Oct 23, 2023
 #3
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S: 1p = 5u - 50

F: 4p = 8u - 8

    1p = 2u - 2

5u - 50 = 2u - 2

   3u = 48

   1u = 16

Shells in the end = 2(16) - 2.

Number of shelsss in end = 30

 Oct 24, 2023

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