Answer:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \sf Pizza & \sf Drinks\\\cline{1-2} \vphantom{\dfrac12} 0& 30\\\cline{1-2} \vphantom{\dfrac12} 1& 20\\\cline{1-2} \vphantom{\dfrac12} 2& 10\\\cline{1-2} \vphantom{\dfrac12} 3& 0\\\cline{1-2} \end{array}[/tex]
See attachment for the graph of the inequality.
Step-by-step explanation:
Given information:
- Maximum amount of money available = $30
- Cost of one large pizza (p) = $10
- Cost of one drink (d) = $1
The inequality to represent the given information is:
To complete the given table, input p from 0 through 3 into the inequality and solve for d.
[tex]\begin{aligned}p=0 \implies 10(0) + d & \leq 30\\d & \leq 30\end{aligned}[/tex]
[tex]\begin{aligned}p=1 \implies 10(1) + d & \leq 30\\10+d & \leq 30\\d & \leq 20\end{aligned}[/tex]
[tex]\begin{aligned}p=2 \implies 10(2) + d & \leq 30\\20+d & \leq 30\\d & \leq 10\end{aligned}[/tex]
[tex]\begin{aligned}p=3 \implies 10(3) + d & \leq 30\\30+d & \leq 30\\d & \leq 0\end{aligned}[/tex]
Completed table:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \sf Pizza & \sf Drinks\\\cline{1-2} \vphantom{\dfrac12} 0& 30\\\cline{1-2} \vphantom{\dfrac12} 1& 20\\\cline{1-2} \vphantom{\dfrac12} 2& 10\\\cline{1-2} \vphantom{\dfrac12} 3& 0\\\cline{1-2} \end{array}[/tex]
To graph the inequality:
- Let the x-axis represent the number of pizzas (p).
- Let the y-axis represent the number of drinks (d).
- Plot two points from the table: (0, 30) and (3, 0).
- Draw a solid line through the points.
- Shade under the line.
