A hairstylist

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 daily for five days weekly. How many appointments can the hairstylist schedule weekly if each customer must be trimmed and styled?

Correct answer:

n =  25

Step-by-step explanation:

$$\begin{gathered} a=\frac{1}{4}+\frac{1}{6}=\frac{3}{12}+\frac{2}{12}=\frac{3+2}{12}=\frac{5}{12}\doteq 0.4167\text{h} \\ b=2\frac{1}{3}=2+\frac{1}{3}=\frac{2\cdot 3+1}{3}=\frac{6+1}{3}=\frac{7}{3}=2\frac{1}{3}\doteq 2.3333\text{h} \\ {n}_1=\lfloor b/a\rfloor =\lfloor 2.3333/0.4167\rfloor =5 \\ n=5\cdot n_1=5\cdot 5=25 \end{gathered}$$

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