Solution:
A family of 3 children and 2 adults visited a health club. The club charges $y an hour for each child and $x an hour for each adult.
First we make inequality according to question.
In a family number of children 3
Charge for 1 child = $y per hour
Charge for 3 children = 3y
Charge for 1 Adult = $x per hour
Charge for 2 adults = 2x
If the family does not want to s[end more than $30 an hour at health club.
[tex]\therefore 2x+3y\leq 30[/tex]
Where, x and y should be greater than 0.
[tex]\therefore x\geq 0,y\geq 0[/tex]
Now we make the graph of this inequality.
First we take equality of equation and then find x and y table.
2x+3y=30
x y
0 10
6 6
15 0
Here we have inequality. So, we have to take a test point (0,0)
[tex]2(0)+3(0)\leq 30\Rightarrow 0\leq 30[/tex]
This statement is true. So, Graph will shade towards the test point (0,0)
Please see the attachment for graph.
