Question

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?

Answer 1

`\bf 21(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 }(2)/(3)\textit{ of that?}\quad \cfrac{85}{4}\cdot \cfrac{2}{3}\implies \cfrac{85}{6}`


`\bf \textit{how many times does }\stackrel{burgers}{(1)/(4)}\textit{ goes into }(85)/(6)?\quad \cfrac{\quad (85)/(6)\quad }{(1)/(4)}\implies \cfrac{85}{6}\cdot \cfrac{4}{1} \\\\\\ \cfrac{170}{3}\implies \stackrel{burgers}{168(2)/(3)}`

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

Answer 2

He made 43 burgers.

Explanation:

Total amount of the ground beef
`=21(1)/(2)` lb.
`=(43)/(2)` lb.

He used
`(1)/(4)` of the beef to make tacos. So, the amount of beef needed to make tacos
`=(1)/(4)((43)/(2))=(43)/(8)` lb.

The amount of remaining beef
`=(43)/(2)-(43)/(8)=(172-43)/(8)=(129)/(8)` lb.

So, the amount of beef needed to make burgers
`=(2)/(3)((129)/(8))=(43)/(4)` lb.

Suppose, the number of quarter pound burgers
`=x`

So, the equation will be.....

`(1)/(4)x=(43)/(4)\\ \\ x=(43)/(4)* (4)/(1)\\ \\ x=43`

Thus, he made 43 burgers.