SOLUTION: Jamal has a collection of bugs. all of them are either ladybugs or spiders. he has a total of 27 bugs. altogether they have 194 legs. how many ladybugs and spiders does he have?

Question 74954: Jamal has a collection of bugs. all of them are either ladybugs or spiders. he has a total of 27 bugs. altogether they have 194 legs. how many ladybugs and spiders does he have? justify you answer.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

Let x=number of ladybugs--------------------------ladybugs have 6 legs
And y=number of spiders------------------------spiders have 8 legs
Now we are told that(number of bugs):
x+y=27------------------------eq 1 (subtract y from both sides)
x=27-y
Now we are also told that(number of legs):
6x+8y=194-----------------------eq 2
We'll solve by substitution. Substitute x=27-y from eq 1 into eq 2
6(27-y)+8y=194 get rid of parens
162-6y+8y=194 subtract 162 from both sides
162-162-6y+8y=194-162 collect like terms
2y=32 divide both sides by 2
y=16-------------------------------------------# of spiders
substitute y=16 into eq 1 and we have:
x=27-16=11--------------------------------------# of ladybugs
CK
11*6+16*8=194
66+128=194
194=194
Hope this helps------ptaylor

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