Solving/Interpreting Linear Inequalities in Two Variables

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

Luka and Dana are making cookies for the Westland Pantry. They only have up to 8 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which region represents less than 8 hours baking?

• Red

• Blue

• Purple (overlap of red and blue)

• Non- Shaded

The members of a new band want to spend no more than $75 for at least 60 fliers to advertise their upcoming concert.  Color fliers cost $1.50 each and black and white fliers cost $0.75 each. Using this criteria, which of the following flier combinations could they order?

• 26 color, 30 black and white

• 30 color, 32 black and white

• 35 color, 35 black and white

• 32 color, 40 black and white

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

To save money for prom this weekend, Tom is going to walk his neighbor's dog for $6 per hour and wash cars for $7.50 per hour. His mother said he can work no more than 15 hours to ensure he keeps up with his homework. Tom needs to make at least $75 to cover prom expenses. If d represents the number of hours walking his neighbor's dog and c represents the number of hours washing cars, which system of inequalities represents this situation?

A group of friends will buy at most 8 snacks at the movie theatre and spend no more than $42. They will pay $4 for each box of candy and $7 for each bag of popcorn. Which combination of boxes of candy and bags of popcorn could 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 bag of popcorn

Select an inequality that shows the constraint on the amount of apples Lexie has to make cobblers and pies.

Sebastian has x nickels and y pennies. He has at least 20 coins worth at most $0.65 combined. Write a system of inequalities.

• x+y<20

  0.05x+0.01y≤0.65

• 0.05x+0.01y>20

  x+y≥0.65

• x+y<0.65

  0.05x+0.1y>0.65

• x+y≥20

  0.05x+0.01y≤0.65