[tex]Ratio:\ \ \frac{1}{10}\\\\x-number\ of\ adults\\477+x-number\ of\ students\\\\If\ ratio\ is\ \frac{1}{10}, for\ 1\ adult\ is\ 10\ students.\ So\ for\ x\ adults\ is\ 10x\\students.\\\\10x=477+x\ \ \ \ \ \ |substract\ x\\10x-x=477\\9x=477\ \ \ \ |:9\\x=53\\\\10x=10\cdot53=530\\\\There\ were\ 53\ adults\ and\ 530\ students.[/tex]