To determine how many pencils each of Sebastian's 6 friends will receive from his 30-pack of mechanical pencils, we need to set up an equation that relates the total number of pencils to the number each friend will receive.
Let's denote [tex]\( p \)[/tex] as the number of pencils each friend will get. Since there are 6 friends, the total number of pencils can be represented as [tex]\( p \)[/tex] multiplied by 6. This should equal the total number of pencils Sebastian has, which is 30.
Mathematically, this relationship can be described by the equation:
[tex]\[ 6p = 30 \][/tex]
Therefore, the equation Sebastian can use to find [tex]\( p \)[/tex] is:
[tex]\[ 6p = 30 \][/tex]
None of the equations provided directly matches this form. However, by studying the given options:
1. [tex]\( p + 6 = 30 \)[/tex]
2. [tex]\( p - 6 = 30 \)[/tex]
3. [tex]\( 60 = 30 \)[/tex]
4. [tex]\( \frac{p}{6} = 30 \)[/tex]
We can see that option 4 correctly positions [tex]\( p \)[/tex] in the context of dividing the total number of pencils (30) by the number of friends (6).
Thus, the equation [tex]\( \frac{p}{6} = 30 \)[/tex], equivalent to multiplying both sides by 6, is:
[tex]\[ p = 5 \][/tex]
So, each friend will receive 5 pencils, confirming that:
[tex]\[ \frac{\rho}{6} = 30 \][/tex]
Given these options, the correct equation that represents the distribution of pencils is:
[tex]\[ \frac{\rho}{6} = 30 \][/tex]
