Question

Ann needs 3/4 of a book in 2 days. At this rate how many books can she read in 4 1/3 days.

Answer 1

`\bf \begin{array}{ccll} book&days\\ \cline{1-2}\\ (3)/(4)&2\\\\ x&4(1)/(3) \end{array}\implies \cfrac{~~(3)/(4)~~}{x}=\cfrac{~~2~~}{4(1)/(3)}\implies \cfrac{~~(3)/(4)~~}{x}=\cfrac{~~2~~}{(13)/(3)} \implies \cfrac{~~(3)/(4)~~}{(x)/(1)}=\cfrac{~~(2)/(1)~~}{(13)/(3)}`

`\bf \cfrac{3}{4}\cdot \cfrac{1}{x}=\cfrac{2}{1}\cdot \cfrac{3}{13}\implies \cfrac{3}{4x}=\cfrac{6}{13}\implies 39=24x\implies \cfrac{39}{24}=x\implies \cfrac{13}{8}=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 1(5)/(8)=x~\hfill`