Question

Daryl's Oreo factory is able to produce 3/4 tons of Oreos in 1 1/2 weeks. At this rate, how long will it take to produce 2

tons of Oreos?

Answer 1

`\bf \begin{array}{ccll} tons&weeks\\ \cline{1-2}\\ (3)/(4)&1(1)/(2)\\\\ 2&x \end{array}\implies \cfrac{~~(3)/(4)~~}{2}=\cfrac{~~1(1)/(2)~~}{x}\implies \cfrac{~~(3)/(4)~~}{2}=\cfrac{~~(3)/(2)~~}{x}\implies \cfrac{~~(3)/(4)~~}{(2)/(1)}=\cfrac{~~(3)/(2)~~}{(x)/(1)} \\\\\\ \cfrac{3}{4}\cdot \cfrac{1}{2}=\cfrac{3}{2}\cdot \cfrac{1}{x}\implies \cfrac{3}{8}=\cfrac{3}{2x}\implies 6x=24\implies x=\cfrac{24}{6}\implies x=4`