Step 1
Convert mixed number to an improper fraction
[tex]21\frac{1}{2}\ lb= \frac{21*2+1}{2} =\frac{43}{2}\ lb[/tex]
Step 2
Find the total pounds used in tacos
we know that
Saeed used [tex]1/4[/tex] of the beef to make tacos
so
[tex]\frac{1}{4}*\frac{43}{2}=\frac{43}{8}\ lb[/tex]
Step 3
Find how many burgers did Saeed make
we know that
Saeed used [tex]2/3[/tex] of the remainder to make quarter-pound burgers
Remember that
If Saeed used [tex]1/4[/tex] of the beef to make tacos
then
the remainder is [tex]3/4[/tex] of the beef
so
[tex]remainder=\frac{3}{4}*\frac{43}{2}=\frac{129}{8}\ lb[/tex]
Multiply the remainder by [tex]2/3[/tex]
[tex]\frac{2}{3}*\frac{129}{8}=\frac{129}{12}\ lb[/tex]
Divide by [tex]1/4[/tex] to find the number of burgers
[tex]\frac{(129/12)}{(1/4)} =\frac{129}{3}=43\ burgers[/tex]
therefore
the answer is
[tex]43\ burgers[/tex]
