Certainly! Let's break down the problem step-by-step to determine how many fence posts are needed for a garden with 112 panels.
We are given the formula for the number of posts [tex]\( n \)[/tex]:
[tex]\[ n = \frac{p}{8} + 5 \][/tex]
where [tex]\( p \)[/tex] is the number of fence panels and [tex]\( n \)[/tex] is the number of posts.
In this problem, we are given [tex]\( p = 112 \)[/tex] fence panels. Let's substitute [tex]\( p \)[/tex] into the formula and solve for [tex]\( n \)[/tex].
1. Start with the given formula:
[tex]\[ n = \frac{p}{8} + 5 \][/tex]
2. Substitute [tex]\( p = 112 \)[/tex] into the formula:
[tex]\[ n = \frac{112}{8} + 5 \][/tex]
3. Divide 112 by 8:
[tex]\[ \frac{112}{8} = 14 \][/tex]
4. Add 5 to the result:
[tex]\[ 14 + 5 = 19 \][/tex]
Therefore, the number of fence posts needed is:
[tex]\[ n = 19 \][/tex]
So, for a garden with 112 panels, you will need 19 fence posts.
