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Recognizing Points Along Boundary Line

2.12.4 Recognizing Points Along Boundary Line

2.12.4 • Recognizing Points Along Boundary Line

Activity

For questions 1 – 6, use the following scenario:

A popular band is trying to raise at least $20,000 for charity by holding multiple concerts at a park. It plans to sell tickets at $25 each. For each 2-hour concert, the band would need to pay the park $1,250 in fees for security, cleaning, and traffic services.

The band needs to find the combinations of number of tickets sold, tt, and number of concerts held, cc, that would allow it to reach its fundraising goal.

1.

Write an inequality to represent the constraints in this situation.

Compare your answer:

25t−1,250c≥20,00025t−1,250c≥20,000

2.

Use the graphing tool or technology outside the course. Graph your inequality from question 1 that represents this scenario using the Desmos tool below.

Access multimedia content

Compare your answer:

The graph of an inequality in the first quadrant. The x-axis represents the number of tickets sold and the y-axis represents the number of concerts held.
3.

Name two possible combinations of number of tickets sold and number of concerts held that would allow the band to meet its goal.

Compare your answer:

  • (1000,2)(1000,2)
  • (1400,5)(1400,5)

For questions 4 – 6, decide which combination of tickets and concerts would mean more money for charity:

4.

1,300 tickets and 10 concerts, or 1,300 tickets and 5 concerts?

Compare your answer:

1,300 tickets and 5 concerts

5.

1,600 tickets and 16 concerts, or 1,200 tickets and 9 concerts?

Compare your answer:

1,600 tickets and 16 concerts.

6.

2,000 tickets and 4 concerts, or 2,500 tickets and 10 concerts?

Compare your answer:

2,500 tickets and 10 concerts