Question

the ratio of participants on the girls track team to the number of boys on the track team is 5:7. If the boys have 22 more participants than the girls, how many girls are on the track team?

Answer 1

$\bf girls:boys\qquad 5:7\qquad \cfrac{girls}{boys}=\cfrac{5}{7}\qquad ~\hspace{8em}\cfrac{\stackrel{\textit{girls}}{g}}{\underset{\textit{22 more than \underline{g}}}{g+22}}=\cfrac{5}{7} \\\\\\ 7g=5(g+22)\implies 7g=5g+110\implies 2g=110\implies g=\cfrac{110}{2}\implies g=55$