Solving/interpreting linear inequalities in two variables

How many of each purse should Sarah make to maximize profit?

• 6 big purses
• 8 small purses
• 6 small purses and 2 big purses

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

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

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

• 2700

• 2650

• 2500

• 2450

• 2300

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.

• $x+y\ge1000$

• $x+y\le1000$

• $y>2x$

• $y\ge2x$

• $x>2y$

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

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?