We know that Karen operates a hot dog stand. So we have:
On Wednesday:
[tex]\text{She used} \ 9 \frac{1}{3} \ \text{bags of hot dog buns.}[/tex]
On Thursday:
[tex]\text{She used} \ \frac{1}{3} \ \text{as many hot dog buns as on Wednesday}[/tex]
Therefore, if x is the amount of hot dog buns she used on Thursday, then:
[tex]x=\frac{1}{3}(9\frac{1}{3}) \\ \\ x=\frac{1}{3}\times 9+\frac{1}{3}\times \frac{1}{3} \\ \\ x=\frac{28}{9}[/tex]
Therefore, on Thursday she used 28/9 bags of hot dog buns.