My collection of spiders and beetles has 8 heads and 54 legs. How many are there of each?

Question

My collection of spiders and beetles has 8 heads and 54 legs. How many are there of each?

Answer 1

S = number of spiders with 8 legs and 1 head each

B = number of beetles with 6 legs and 1 head each

 

(i)  S + B = 8  [8 heads total]

(ii) 8S + 6B = 54  [54 legs total]

 

From (i) get S = 8 - B and substitute into (ii) to get B.

 

8(8 - B) + 6B = 54 

64 - 8B + 6B = 54

10 = 2B

B = 5

 

S = 8 - B = 8 - 5 = 3

 

There are 3 spiders and 5 beetles.