Answer
See below:
Work Step by Step
(a)
A number of children be x and adults be y. Total weight of children and adults will be \[50x+150y\]pounds on the elevator. The elevator will be overloaded if weight exceeds 2000 pounds,
\[50x+150y>2000\]
(b)
The y-intercept is
\[\begin{align}
& 150y>2000 \\
& y>13.33
\end{align}\]
The x-intercept is
\[\begin{align}
& 50x>2000 \\
& x>40
\end{align}\]
Connect the points to form a line. Note the dashed line, since 2000 pounds is not included. No more than 40 children or 13 adults can get into the elevator.
(c)
The graph of the inequality \[50x+150y>2000\] with ordered-pair \[\left( 25,10 \right)\]
Select any point in the shaded region to satisfy the inequality
The ordered-pair \[\left( 25,10 \right)\] states that there will be 25 children and 10 adults.
Applying the values in the inequality,
\[\begin{align}
& 50x+150y>2000 \\
& 50\left( 25 \right)+150\left( 10 \right)>2000 \\
& 2750>2000
\end{align}\]
If there were 25 children and 10 adults to take up an elevator, it would be overloaded.
