28 appointments can be scheduled each week if each customer must be trimmed and styled
Solution:
From given,
[tex]Time\ to\ trim\ hair = \frac{1}{4}\ hour[/tex]
[tex]Time\ to\ style\ hair = \frac{1}{6}\ hour[/tex]
Therefore, total time taken for each customer hair to be trimmed and styled is:
[tex]Total\ time = \frac{1}{4} + \frac{1}{6} = \frac{6+4}{24} = \frac{10}{24}\ hours\\\\Convert\ to\ minutes\\\\1\ hour = 60\ minutes\\\\Therefore\\\\\frac{10}{24}\ hour = \frac{10}{24} \times 60\ minutes = 25\ minutes[/tex]
Thus, each customer trim and style = 25 minutes
Given that,
The hairstylist plans to work 2 1/3 hours each day for 5 days each week
Then, for 5 days, the hairstyist will work for:
[tex]Total\ working\ time\ of\ hairstylist = 2\frac{1}{3} \times 5\ hours\\\\\rightarrow \frac{7}{3} \times 5\ hour\\\\Convert\ to\ minutes\\\\\rightarrow \frac{7}{3} \times 5 \times 60\ minutes = 700\ minutes[/tex]
Thus hairstylist will work for 700 minutes each week
Total number of appointments:
Total number of appointments for each week is found by dividing the working time of hair stylist for each week divided by time spent for each customer for trim and styled
[tex]Number\ of\ appointment = \frac{700}{25} = 28[/tex]
Thus 28 appointments can be made
