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

Answer:

He made 43 burgers.

Step-by-step explanation:

Total amount of the ground beef $=21\frac{1}{2}$ lb. $=\frac{43}{2}$ lb.

He used $\frac{1}{4}$ of the beef to make tacos. So, the amount of beef needed to make tacos  $=\frac{1}{4}(\frac{43}{2})=\frac{43}{8}$ lb.

The amount of remaining beef  $=\frac{43}{2}-\frac{43}{8}=\frac{172-43}{8}=\frac{129}{8}$ lb.

So, the amount of beef needed to make burgers  $=\frac{2}{3}(\frac{129}{8})=\frac{43}{4}$ lb.

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

So, the equation will be.....

$\frac{1}{4}x=\frac{43}{4}\\ \\ x=\frac{43}{4}\times \frac{4}{1}\\ \\ x=43$

Thus, he made 43 burgers.

Answer 2

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

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

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