Question 1048118
F = number of female bugs
M = number of male bugs



"there are 10% more female bugs than male bugs" means that {{{F = 0.1*M+M}}} which turns into {{{F = 1.1M}}}



" there are 8 more females than males" means {{{F = M+8}}}



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



{{{F = M+8}}} Start with the second equation



{{{1.1M = M+8}}} Replace F with 1.1M (see above)



{{{1.1M-M = M+8-M}}} Subtract M from both sides



{{{0.1M = 8}}} Combine like terms



{{{0.1M/0.1 = 8/0.1}}} Divide both sides by 0.1 to isolate M



{{{M = 80}}} Simplify



There are 80 male bugs



{{{F = M+8}}} Go back to the second equation above



{{{F = 80+8}}} Replace M with 80



{{{F = 88}}} Add



There are 88 female bugs



There are a total of 80+88 = 168 bugs