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