Question

The spiders and ants in Aunt Mellys attic have a total of 152 legs and 22 heads. Spiders have 8 legs and ants have 6 legs. How many spiders and how many ants are in the attic?

Answer 1

10 spiders and 12 ants

Explanation:

You need to create two equations

s = # of spiders

a = # of ants

s + a = 22 heads

since each spider and ant has one head

8s + 6a = 152 legs

since every spider has 8 legs and every ant has 6

s + a = 22 can be turned into s = 22 - a

now use substitution

8(22 - a) + 6a = 152

176 - 8a + 6a = 152

176 - 2a = 152

24 = 2a

a = 12

now that you have the number of ants you can solve for the number of spiders

s + a = 22

s + 12 = 22

s = 10