Question

A hairstylist schedules 1/4 hour to trim a customer’s hair and 1/6 hour to style the customer’s hair. The hairstylist plans to work 2 1/3 hours each day for 5 days each week. How many appointments can the hairstylist schedule each week if each customer must be trimmed and styled

Answer 1

28 appointments can be scheduled each week if each customer must be trimmed and styled

Solution:

From given,

$Time\ to\ trim\ hair = \frac{1}{4}\ hour$

$Time\ to\ style\ hair = \frac{1}{6}\ hour$

Therefore, total time taken for each customer hair to be trimmed and styled is:

$Total\ time = \frac{1}{4} + \frac{1}{6} = \frac{6+4}{24} = \frac{10}{24}\ hours\\\\Convert\ to\ minutes\\\\1\ hour = 60\ minutes\\\\Therefore\\\\\frac{10}{24}\ hour = \frac{10}{24} \times 60\ minutes = 25\ minutes$

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:

$Total\ working\ time\ of\ hairstylist = 2\frac{1}{3} \times 5\ hours\\\\\rightarrow \frac{7}{3} \times 5\ hour\\\\Convert\ to\ minutes\\\\\rightarrow \frac{7}{3} \times 5 \times 60\ minutes = 700\ minutes$

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

$Number\ of\ appointment = \frac{700}{25} = 28$

Thus 28 appointments can be made