Solving Systems of Linear Inequality Word Problems

Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

• x + y ≤ 300
  7.5x + 5.5y ≥ 2000

• x + y < 300
  7.5x + 5.5y ≥ 2000

• x + y ≤ 300
  7.5x + 5.5y ≤ 2000

• x + y > 2000
  7.5x + 5.5y ≤ 300

Jonah is going to the store to buy candles. Small candles cost $3.50, and large candles cost $5.00. He needs to buy at least 20 candles and cannot spend more than $80.

Write a system of linear inequalities that represents the situation.

Gabriela is the manager of a print shop. She needs to schedule employees to work no more than 300 person-hours per week. She has one 20 hour a week part-time employee. Each full-time employee works 40 hours per week. Which inequality will determine f, the number of full-time employees Gabriela can schedule to remain under the 300 person-hour per week limit?

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. 

• 7x + 13y < 81

• 7x + 13y ≥ 81

• 7x + 13y ≤ 81

• 7x + 13y > 81

Which of the following is a solution to the systems of inequalities?

• (0, 0)

• (-3, 0)

• (2, -5)

• (3, -1)

Which of the following is a solution to the systems of inequalities?

• (0, -2)

• (-3, 0)

• (-3, 2)

• (1, 1)

Write the linear inequality in standard form for this situation: In order to raise money to attend upcoming competitions, the Math Pentathalon team is selling apple cider and hot chocolate. They hope to make at least $240 by selling hot chocolate for $1 a glass and hot apple cider for $2 a glass.

• x + 2y < 240

• x + 2y > 240

• x + 2y ≤ 240

• x + 2y ≥ 240

Write the linear inequality in standard form for this situation: The manager of an electronics store projects that the store should achieve more than $21,000 in revenue from TVs and DVD players every day in order to remain profitable. Tvs sell for $225 and DVD players sell for $175.

• 225x +175y ≤ 21,000

• 225x +175y ≥ 21,000

• 225x +175y < 21,000

• 225x +175y > 21,000

Two seventh-grade classes are selling raffle tickets to raise money.
-One class is selling tickets for $3.50 each and has already raised $400.
-The other class is selling  tickets for $2.00 each and has already raised $300.
Which equation can be used to find m, the number of tickets each class needs to sell so that the total amount raised is the same for both classes?

• 5.5m = 700

• 3.50m = 2m + 300

• 3.5m + 400 = 2m + 300

• 3.5 + 400m = 2 + 300m

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