Saeed bought 21 1/2 lb. of ground beef. he used 1/4 of the beef to make tacos and the remaining 2/3 of the remainder to make quarter pound burgers. how many burgers did he make?

[tex]\bf 21\frac{1}{2}\implies \cfrac{21\cdot 2+1}{2}\implies \cfrac{43}{2}\\\\ -------------------------------\\\\ \cfrac{43}{2}~-\stackrel{for~tacos}{\cfrac{1}{4}}\implies \cfrac{86-1}{4}\implies \stackrel{remainder}{\cfrac{85}{4}} \\\\\\ \textit{how much is }\frac{2}{3}\textit{ of that?}\quad \cfrac{85}{4}\cdot \cfrac{2}{3}\implies \cfrac{85}{6}[/tex]

[tex]\bf \textit{how many times does }\stackrel{burgers}{\frac{1}{4}}\textit{ goes into }\frac{85}{6}?\quad \cfrac{\quad \frac{85}{6}\quad }{\frac{1}{4}}\implies \cfrac{85}{6}\cdot \cfrac{4}{1} \\\\\\ \cfrac{170}{3}\implies \stackrel{burgers}{168\frac{2}{3}}[/tex]

so.. hmm whole 1/4 lbs burgers, is just 168.