Solving Inequalities in Two Variables

The total amount of your electric (x) and water (y) bill is at most 3000 pesos. Which of the following correctly represents this situation?

• x + y ≥ 3000

• x + y ≤ 3000

• x + y > 3000

• x + y < 3000

Based on question #2, If your electric bill (x) is 2200 pesos, what could be the cost of your water bill (y)?

• y < 800; The water bill is less than 800 pesos

• y > 800; The water bill is more than 800 pesos

• y ≤ 800; The water bill is at most 800 pesos

• y ≥ 800; The water bill is at least 800 pesos

A jar contains 20 peso bills (x) and 50 peso bills (y). The sum of the money is less than 500 pesos. Which of the following correctly represents this situation?

• 20x + 50y ≥ 500

• 20x + 50y ≤ 500

• 20x + 50y > 500

• 20x + 50y < 500

At the Big Bear video rental store, blank CDs cost $1.50 each and blank DVDs cost $3.25 each.  Which of the following statements best describes the number of CDs (c) and DVDs (d) that can be purchased for less than $65.00?

• 1.50c + 3.25d < 65.00

• 3.25c + 1.50d <65.00

• 1.50c + 3.25d ≤ 65.00

• 3.25c + 1.50d ≤ 65.00

A group of friends will buy at most 8 snacks at the movie theater and spend no more than $42.  They will pay $4 for each box of candy and $7 for each tub of popcorn.  The system of inequalites that represents the situation is:
x + y <= 8 
4x + 7y <= 42 
Which combination of candy and popcorn can the group buy? 

• 2 boxes of candy and 6 bags of popcorn 

• 3 boxes of candy and 4 bags of popcorn

• 5 boxes of candy and 4 bags of popcorn

• 8 boxes of candy and 1 bags of popcorn

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

Write the system of inequalities
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

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. She will make $4000 profit per acre of soybeans and $3000 per acre of corn. If x represents acres of soybeans and y represents acres of corns, which inequalities represent the constraints to her situation?

Tags

A2.ACE.3

SMJK JIT SIN II holds a charity concert in a hall. Two types of concert ticket, VIP and Special, will be sold among parents. The number of VIP ticket sold is x and the number of Special ticket sold is y. The hall can provide not more that 1000 seats. The number of Special tickets must exceed twice the number of VIP tickets.

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The farmer profits $4000 for every acre of soybeans and $3000 for every acre of corn. If x = acres of soybeans and y = acres of corn, which inequalities represent the possible solutions to her situation?

• x≥0

  y≥0

  x+y≥6

  3x+2y≥15

• x≥0

  y≥0

  x+y≤6

  2x+3y≤15

• x≥0

  y≥0

  4000x+y≤6

  2x+600y≤15

• P=4000x+3000y