QQuestionMathematics
QuestionMathematics
2. A radio station is giving away tickets to a play. They plan to give away tickets for seats that cost $\$ 1$ and $\$ 1$. They want to give away at least 20 tickets. The total cost of all the tickets they give away can be no more than $\$ 1$. Use a graph to determine possible outcomes.
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Answer
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Step 1:: Define the variables and constraints.
10x + 20y \leq 280 \tag{2}
The radio station wants to give away at least 20 tickets, so:
Step 2:: Solve for y in inequality (1).
y \geq 20 - x \tag{3}
Step 3:: Plot the constraint lines on a graph.
Plot both lines on a graph, labeling the x-axis as "Number of $\$10$ Tickets (x)" and the y-axis as "Number of $\$20$ Tickets (y)".
The constraint lines are given by inequalities (2) and (3). For inequality (2), solve for y: The feasible region is the area below the line given by inequality (4) and above the line given by inequality (3).
Step 4:: Determine possible outcomes.
These points represent the number of $\$10$ and $\$20$ tickets the radio station can give away while satisfying their constraints.
The possible outcomes are the points in the feasible region that correspond to whole numbers for both x and y.
Final Answer
The possible outcomes are the points in the feasible region that correspond to whole numbers for both x and y, which can be determined by analyzing the graph.
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