She had a total of $34 to spend on art supplies.
She purchased a sketchbook for $13.5 and 4 charcoal pencils each one for the same x price.
She had $11.30 left in change.
With the situation above, we can create the following equations:
Let x be the price of each charcoal pencil
[tex]\begin{gathered} 13.5+4x+11.30=34 \\ 4x+24.8=34 \\ 4x=34-24.8 \\ x=\frac{9.2}{4} \\ x=2.3 \end{gathered}[/tex]
Each charoal pencil costs $2.3.