the boutique buys the dress at $120 and then marks it up 35%, then we have the following:
[tex]\begin{gathered} \text{ \$120 with 35\% up} \\ \text{ Then we must calculate the 135\% of \$120:} \\ (120)(1.35)=162 \end{gathered}[/tex]Afterwards, the dress went on sale for 20% off, then:
[tex]\begin{gathered} \text{ 20\% discount of \$162} \\ \Rightarrow(162)\cdot(0.80)=129.60 \end{gathered}[/tex]Therefore, the purchase price of the dress is $129.60