Graphing and Systems of Linear Inequalities

A movie theater is selling movie tickets for 7pm show. The theater needs to sell at least $400 worth of tickets. Each adult ticket, x, costs $12 and each child ticket, y, costs $10. Which ordered pair represents a possible number of adult and child tickets that can be sold?

• (10, 20)

• (25, 12)

• (9, 27)

• (20, 14)

Suzy is buying In-N-Out Burger for lunch for her friends.  The hamburgers cost $3.50 each and the drinks cost $1.50 each.  She wants to spend no more than $30 on lunch. 

This information is represented using the inequality: 3.5h + 1.5d ≤ 30, where the drinks(y) and the hamburgers(x)

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Which point is a solution?

• (0, 6)
• (-3, 4)
• (1, 0)
• (-4, 3)

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

• 2x + 3y > 100

  x + y ≤ 40

• 100x + 2y > 3

  x + y ≤ 40

• 100x + 40y > 100

  3x + 2y ≤ 40

• 3x + 2y > 100

  x + y ≤ 40

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?

• b + t < 15
  3b + 6t > 66
• b + t > 15
  3b + 6t < 66
• 3b + 6t > 15
  b + t < 66
• 3b + 6t < 15
  b + t < 66

Solve the system of inequalities by graphing.

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Identify the graph represented by the following system of inequalities.

2x - y > 4

4x + 2y < 6

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The members of a new band want to spend no more than $75 for at least 60 fliers to advertise their upcoming concert.  The cost color fliers is $1.50 each, the cost of black and white fliers is $0.75 each. Which of the following combinations is a reasonable solution?

• 26 color, 30 black and white
• 30 color, 35 black and white
• 60 color
• 30 color, 50 black and white

Write the linear inequality in standard form for this situation: Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than $81. An order of breadsticks costs $7 and a pizza costs $13. 

Which graph matches the situation?

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