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# An entomologist

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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?

May 6, 2015

#1
+27915
+10

Larva:    1 head  0 legs (?)

S + B + L = 17  ...(1)

S + B > L          ...(2)

8S + 6B = 58    ...(3)

Solving (1) and (3) for S and B we get

S = 3L - 22   ...(4)

B = 39 - 4L   ...(5)

From (4) we see that L must be greater than 7 or S will be negative.

Try L = 8

S = 2,   B = 7    and S + B = 9 which is greater than L consistent with (2)

Try L = 9

S = 5, B = 3   and S + B = 8 which is less than L so not consistent with (2)

L must be less than 10 or B will be negative

Therefore there must be 2 spiders (and 7 beetles and 8 larvae).

.

May 6, 2015

#1
+27915
+10

Larva:    1 head  0 legs (?)

S + B + L = 17  ...(1)

S + B > L          ...(2)

8S + 6B = 58    ...(3)

Solving (1) and (3) for S and B we get

S = 3L - 22   ...(4)

B = 39 - 4L   ...(5)

From (4) we see that L must be greater than 7 or S will be negative.

Try L = 8

S = 2,   B = 7    and S + B = 9 which is greater than L consistent with (2)

Try L = 9

S = 5, B = 3   and S + B = 8 which is less than L so not consistent with (2)

L must be less than 10 or B will be negative

Therefore there must be 2 spiders (and 7 beetles and 8 larvae).

.

Alan May 6, 2015
#2
+101761
+5

You have repeated this question without stating that it is a repeat question.

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

There is not time to answer all!

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

My solution is here:

http://web2.0calc.com/questions/question-3

May 6, 2015
#3
+101234
0

Vey nice, Melody and Alan.....

May 6, 2015