solving a system of inequalities graphically - A hairstylist charges $25 for an adult haircut and $15 for a child haircut. She wants to earn at least $450 dollars and cut a maximum of 20 haircuts this week. The graphs represent the hairstylist’s constraints.

Sahil Khan (last edited 2 years ago)

Let x be each adult and y be each child.

The inequality which represent the first constraint or the cost constraint is

25 x + 15 y \geq 450

The inequality which represents the quantity or the number of haircuts is

x + y \leq 20

Take two points on the graph which are a solution or which satisfy both the inequalities (20,0) and (15,5) satisfy both inequalities.

CHECK:

Substitute (15,5) and (20,0) in the inequality,

25 x + 15 y \geq 450

25 \cdot 15 + 15 \cdot 5 \geq 450

450\geq 450

Similarly substitute (20,0) in the inequality to get,

25 \cdot 20 + 15 \cdot 0 \geq 450

450 \geq 450

So, the set of points satisfy the cost constraint.

Similarly the same set of points (15,5) and (20,0) satisfy the quantity constraint.

x + y \leq 20

15 + 5 \leq 20

20 + 0 \leq 20