Question

A certain stylist charges $15 for a haircut and $30 for hair coloring. A haircut takes on average 30 minutes, while coloring takes 2 hours. The stylist works up to 8 hours in a day, and she needs to make a minimum of $150 a day to pay for her expenses.
a. Create a system of inequalities that describes the constraints in this situation. Be sure to specify what each variable represents.

b. Graph the inequalities and show the solution set.

c. Identify a point that represents a combination of haircuts and and hair-coloring jobs that meets the stylist's requirements.

Answer 1

• Haircuts be x
• hair coloring be y

#a

$\\ \sf{:}\Rrightarrow 15x+30y\geqslant 150$

$\\ \sf{:}\Rrightarrow x+y\geqslant 10$

And

$\\ \sf{:}\Rrightarrow 0.5x+2y\geqslant 8$

#2

Attached

#3

• (8,2)