Question

A coffeepot contains 1 1/2 quqarts of coffee. After Tonya pours an equal amount of coffee into two cups, 3 1/2 cups of coffee still remain in the pot. How much coffee did Tonya pour into each cup?

Answer 1

`\bf 1(1)/(2)\implies \cfrac{1\cdot 2+1}{2}\implies \cfrac{3}{2}\quad \textit{now, how much is a quart of that?} \\\\\\ \cfrac{3}{2}\cdot \cfrac{1}{4}\implies \stackrel{of~coffee}{\cfrac{3}{8}}\impliedby makes\quad \stackrel{poured}{2cups}+\stackrel{remaining}{3(1)/(2)cups}\implies 5(1)/(2)~cups`


`\bf \textit{now if }(3)/(8)\textit{ of coffee makes }5(1)/(2)\textit{ cups, how much in 1 cup?} \\\\\\ \cfrac{\quad (3)/(8)\quad }{5(1)/(2)}\implies \cfrac{\quad (3)/(8)\quad }{(5\cdot 2+1)/(2)}\implies \cfrac{\quad (3)/(8)\quad }{(11)/(2)}\implies \cfrac{3}{8}\cdot \cfrac{2}{11}\implies \stackrel{\textit{of coffee makes one cup}}{\cfrac{3}{44}}`