Question

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. If the family does not want to spend more than $30 an hour at the health club, which of the following graphs best models the situation?

Answer 1

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.

`\therefore 2x+3y\leq 30`

Where, x and y should be greater than 0.

`\therefore x\geq 0,y\geq 0`

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)

`2(0)+3(0)\leq 30\Rightarrow 0\leq 30`

This statement is true. So, Graph will shade towards the test point (0,0)

Please see the attachment for graph.