Question

In aunt Peggy's attic, there are spiders and ants. All together have a total of 160 legs. If the number of ants is one greater than the number of spiders, how many spiders and how many ants are there?

Answer 1

Let's start by assigning variables:
Let S = number of spiders
Let A = number of ants

We know that each spider has 8 legs and each ant has 6 legs. We also know that the total number of legs is 160.

So, we can create the following equation:
8S + 6A = 160

We also know that the number of ants is one greater than the number of spiders:
A = S + 1

Now we can substitute A = S + 1 into the first equation:

8S + 6(S + 1) = 160
8S + 6S + 6 = 160
14S + 6 = 160
14S = 154
S = 11

Now that we have found the number of spiders, we can find the number of ants:
A = S + 1
A = 11 + 1
A = 12

Therefore, there are 11 spiders and 12 ants in Aunt Peggy's attic.