SOLUTION: Elizabeth has a collection of bugs. all of them are either fruit flies or tarantulas. she has a total of 75 bugs. altogether they have a total of 562 legs. how many fruit flies an

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Question 74953: Elizabeth has a collection of bugs. all of them are either fruit flies or tarantulas. she has a total of 75 bugs. altogether they have a total of 562 legs. how many fruit flies and tarantulas does she have? justify your answer.
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!

Let x=number of fruit flies---they have 6 legs
And y=number of tarantulas-----they have 8 legs
Now we are told that:
x+y=75------------------------------eq 1 (subtract y from both sides)
x=75-y

We are also told that:
6x+8y=562-----------------------------eq 2
We will solve by substitution. Substitute x=75-y from eq 1 into eq 2
6(75-y)+8y=562 get rid of parens
450-6y+8y=562 subtract 450 from both sides
450-450-6y+8y=562-450 collect like terms
2y=112 divide both sides by 2
y=56-------------------------------------------# of tarantulas
substitute y=56 into eq 1
x+56=75 subtract 56 from both sides
x=75-56
x=19-----------------------------------------# fruit flies
ck
19*6+56*8=562
114+448=562
562=562

Hope this helps -----ptaylor