Question

You and some friends have $30. You want to order large pizzas (p) that are $10 each and drinks (d) that cost $1 each. Make a table of possible choices(including intercepts) and graph an inequality that shows how many pizzas and drinks you can order.

Answer 1

`\begin{array}c\cline{1-2} \vphantom{\frac12} \sf Pizza & \sf Drinks\\\cline{1-2} \vphantom{\frac12} 0& 30\\\cline{1-2} \vphantom{\frac12} 1& 20\\\cline{1-2} \vphantom{\frac12} 2& 10\\\cline{1-2} \vphantom{\frac12} 3& 0\\\cline{1-2} \end{array}`

See attachment for the graph of the inequality.

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:

• 10p + d ≤ 30

To complete the given table, input p from 0 through 3 into the inequality and solve for d.

`\begin{aligned}p=0 \implies 10(0) + d & \leq 30\\d & \leq 30\end{aligned}`

`\begin{aligned}p=1 \implies 10(1) + d & \leq 30\\10+d & \leq 30\\d & \leq 20\end{aligned}`

`\begin{aligned}p=2 \implies 10(2) + d & \leq 30\\20+d & \leq 30\\d & \leq 10\end{aligned}`

`\begin{aligned}p=3 \implies 10(3) + d & \leq 30\\30+d & \leq 30\\d & \leq 0\end{aligned}`

Completed table:

`\begin{array}c\cline{1-2} \vphantom{\frac12} \sf Pizza & \sf Drinks\\\cline{1-2} \vphantom{\frac12} 0& 30\\\cline{1-2} \vphantom{\frac12} 1& 20\\\cline{1-2} \vphantom{\frac12} 2& 10\\\cline{1-2} \vphantom{\frac12} 3& 0\\\cline{1-2} \end{array}`

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.