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An entomologist always keeps a few ‘pets’ at home and currently has some spiders, beatles, and an assortment of apodous larvae. She has less larvae than spiders and beatles combined. Altogether in the collection there are seventeen heads and fifty-eight legs. How many spiders does the entomologist keep?

Guest May 6, 2015

Best Answer 

 #3
avatar+92805 
+5

NOTE:

Equations that can only have integer solutions are call diophantine equations

As a general rule thes are much more difficult to solve than normal equations where all real solutions are acceptable.

---------------------------------------------------

I have just seen a pop-up telling me that you have repeated this question without stating that it is a repeat question.

PLEASE DO NOT DO THIS!!

Alan and i have both answered you and as a result other question will not be answered.

You are invited to repost - that is fine BUT  please follow the intstuctions that i have laid out here.

http://web2.0calc.com/questions/instructions-on-reposting_1

 

Alan's solution is here:

http://web2.0calc.com/questions/an-entomologist

Melody  May 6, 2015
 #1
avatar+92805 
+5

ok

spiders have 8 legs and 1 head               S

beatles have 6 legs and one head            B

apodous larvae have no legs and 1 head     L

S+B+L=17    and     8S+6B=58

 

Lets look at this     8S+6B=58      

number of spiders that there could be             1     2     3     4     5     6     7 

no. of spiders legs                                            8   16   24   32   40   48  56 

legs left for beatles                                         50   42  34   26     18   10  2  

Which of these is divisable by 6?                            42                   18

How many beatles might this be (divide by 6)         7                     3

 

SO there could be     2 spiders 7 beeetles and 8 Lavae

or  there could be     5 spiders  3 beetles and  9 lavae    

                     

She has less lavae than spiders and beetles combined so 

SO there must be     2 spiders 7 beeetles and 8 Lavae

Melody  May 6, 2015
 #2
avatar+26753 
0

This question seems to have been repeated here: http://web2.0calc.com/questions/an-entomologist I answered it earlier, not realising it was a repeat!

.

Alan  May 6, 2015
 #3
avatar+92805 
+5
Best Answer

NOTE:

Equations that can only have integer solutions are call diophantine equations

As a general rule thes are much more difficult to solve than normal equations where all real solutions are acceptable.

---------------------------------------------------

I have just seen a pop-up telling me that you have repeated this question without stating that it is a repeat question.

PLEASE DO NOT DO THIS!!

Alan and i have both answered you and as a result other question will not be answered.

You are invited to repost - that is fine BUT  please follow the intstuctions that i have laid out here.

http://web2.0calc.com/questions/instructions-on-reposting_1

 

Alan's solution is here:

http://web2.0calc.com/questions/an-entomologist

Melody  May 6, 2015

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