Let's start by writing the equation in terms of [tex]\( p \)[/tex], where [tex]\( p \)[/tex] represents the cost of each pencil:
Alan bought 3 pencils and 1 notebook, and the total cost was [tex]$12. We know that the notebook costs $[/tex]6.
So, the equation representing the total cost can be written as:
[tex]\[ 3p + 6 = 12 \][/tex]
Next step is to solve for [tex]\( p \)[/tex]:
1. Subtract 6 from both sides to isolate the term with [tex]\( p \)[/tex]:
[tex]\[ 3p = 12 - 6 \][/tex]
2. Simplify the right-hand side:
[tex]\[ 3p = 6 \][/tex]
3. Divide both sides by 3 to solve for [tex]\( p \)[/tex]:
[tex]\[ p = \frac{6}{3} \][/tex]
4. Simplify:
[tex]\[ p = 2 \][/tex]
Therefore, each pencil costs [tex]$2.
So, the correct answer is:
C. \( 3p + 6 = 12 \Rightarrow p = 2 \); each pencil costs $[/tex]2.
Note: The typo in answer D where it reads [tex]\( p=6 \)[/tex]; each pencil cost [tex]\( \$ 2 \)[/tex] should be disregarded, as it contradicts itself.
