SOLUTION: In a terrarium, there are 10% more female bugs than male bugs. If there are 8 more females than males, how many bugs are in the terrarium?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a terrarium, there are 10% more female bugs than male bugs. If there are 8 more females than males, how many bugs are in the terrarium?      Log On


   

Question 1048118: In a terrarium, there are 10% more female bugs than male bugs. If there are 8 more females than males, how many bugs are in the terrarium?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
F = number of female bugs
M = number of male bugs


"there are 10% more female bugs than male bugs" means that F+=+0.1%2AM%2BM which turns into F+=+1.1M


" there are 8 more females than males" means F+=+M%2B8


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We'll use these equations to find M and F.


F+=+M%2B8 Start with the second equation


1.1M+=+M%2B8 Replace F with 1.1M (see above)


1.1M-M+=+M%2B8-M Subtract M from both sides


0.1M+=+8 Combine like terms


0.1M%2F0.1+=+8%2F0.1 Divide both sides by 0.1 to isolate M


M+=+80 Simplify


There are 80 male bugs


F+=+M%2B8 Go back to the second equation above


F+=+80%2B8 Replace M with 80


F+=+88 Add


There are 88 female bugs


There are a total of 80+88 = 168 bugs