You are putting up a 60 foot long fence in your backyard. According to the manufacturer's instructions, the fence posts should be equally spaced along the length of the yard. List all the possible spacing options if the amount of space between the posts is a whole number of feet. If the posts should be spaced between 8 feet and 14 feet apart, how far apart should your posts be?

First determine all the factors of 60 (prime numbers or composite):

1*60
2*30
3*20
4*15
5*12
6*10

Among the 12 factors (2 per line above), which is the highest (and most economical) number that is between 8 and 14?

10 and 12 are in the middle

10 6 divide by 10

To find the possible spacing options, we need to find the factors of the total length of the fence, which is 60 feet. The factors of 60 are numbers that divide 60 without leaving a remainder.

To determine the factors, you can start by listing pairs of numbers and checking if they evenly divide 60. Here's one way to find the factors:

1 x 60 = 60
2 x 30 = 60
3 x 20 = 60
4 x 15 = 60
5 x 12 = 60
6 x 10 = 60

So, the factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Now, let's identify the factors that fall within the given range of 8 feet to 14 feet apart:

8 is not a factor of 60
9 is not a factor of 60
10 is a factor of 60
11 is not a factor of 60
12 is a factor of 60
13 is not a factor of 60
14 is a factor of 60

Therefore, the possible spacing options for the fence posts are 10 feet and 12 feet apart.

Given that the posts should be spaced between 8 feet and 14 feet apart, the desired spacing for your posts should be 10 feet apart.