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? Line joining ordered pairs 0, 10 and 15, 0. Shade the portion of the graph below this line which lies within the first quadrant Line joining ordered pairs 0, 10 and 15, 0. Shade the portion of the graph above this line which lies within the first quadrant Line joining ordered pairs 0, 15 and 10, 0. Shade the portion of the graph below this line which lies within the first quadrant Line joining ordered pairs 0, 15 and 10, 0. Shade the portion of the graph above this line which lies within the first quadrant

Answer 1

Answer: Line joining ordered pairs (0, 10) and (15, 0) and Shade the portion of the graph below this line which lies within the first quadrant.

Explanation:

Here, The club charges $y an hour for each child and $x an hour for each adult.

And, according to the question,

In the family 3 children and 2 adults visited a health club such that the family does not want to spend more than $30 an hour at the health club.

That is,
`2x + 3y\leq 30`

Which is the required inequality.

Since at origin,
`2* 0 + 3* \leq 30` (true)

That is, the inequality must contains the origin.

Therefore, shaded region will occur below the line.

Also, x-intercept of the given line is (15,0)

And, y-intercept of the given line is (0,10)

Thus the line will join the order pairs (15,0) and (0,10)

Also,
`x\geq 0` and
`y\geq 0` ( because charges can not be negative)

Therefore the shaded region will only contain the first quadrant.