[tex]x\ \ \rightarrow\ \ the\ number\ of\ Soo-Jin's\ beads\\y\ \ \rightarrow\ \ the\ number\ of\ Mary's\ beads\\\\x=y\ \ \ \ \ and\ \ \ \ \ 7\cdot(x-54)=y+54\\\\7x-7\cdot54=x+54\\7x-7\cdot54-x+7\cdot54=x+54-x+7\cdot54\\6x=8\cdot54\ \ /:6\\\\x= \frac{\big{8\cdot54}}{\big{6}} \\\\x= 8\cdot9\\\\x=72\ \ \ \Rightarrow\ \ \ y=72\ \ \ \Rightarrow\ \ \ x+y=2\cdot72=144\\\\Ans.\ \ \ 144\ beads\ altogether[/tex]