Let's solve the equation step-by-step to find the value of [tex]\( y \)[/tex] that makes the equation [tex]\( 3 \cdot y = 32 + y \)[/tex] true.
1. Starting with the given equation:
[tex]\[
3y = 32 + y
\][/tex]
2. Move all terms involving [tex]\( y \)[/tex] to one side of the equation. Subtract [tex]\( y \)[/tex] from both sides:
[tex]\[
3y - y = 32
\][/tex]
3. Combine like terms on the left-hand side:
[tex]\[
2y = 32
\][/tex]
4. Solve for [tex]\( y \)[/tex]. Divide both sides of the equation by 2:
[tex]\[
y = \frac{32}{2}
\][/tex]
5. Simplify the fraction:
[tex]\[
y = 16
\][/tex]
So, the value of [tex]\( y \)[/tex] that makes the equation true is [tex]\( y = 16 \)[/tex].
Therefore, the correct answer is:
[tex]\[
\text{B.}\ 16
\][/tex]
