If the relation between the book read by Alexa and the number of months she takes to read them is directly proportional, then, if x is the number of months she took to read 120 books, you can write:
[tex]\frac{x}{120}=\frac{9}{54}[/tex]By solving for x and simplifying, you obtain:
[tex]\begin{gathered} x=\frac{9}{54}\cdot120 \\ x=20 \end{gathered}[/tex]Hence, Alexa read 120 books in 20 months
