Ordered Pair Satisfies Inequality

The minimum value of x is 12 less than 8 times another number n. Which inequality shows the possible values of x?

A number x is at most 17 less than 5 times the value of y. If the value of y is 5, what is the greatest possible value of x?

Answer explanation

x <= 5 - 17

If y is 3,

x <= 15 - 17

x<= -2

• (-2, -1)

• (-1, 3)

• (1, 5)

• (2, -1)

The point (8, 2) in the xy-plane is a solution to which of the following systems of inequalities?

• x > 0

  y > 0

• x > 0

  y < 0

• x < 0

  y > 0

• x < 0

  y < 0

Answer explanation

x > 0 and y > 0 represents all the points in the first quadrant on the xy-plane (where x and y are positive)

• (1, 0)

• (-1, 0)

• (0, 1)

• (0, -1)

A bakery sells trays of cookies. Each tray contains at least 50 cookies but no more than 60. Which of the following could be the total number of cookies on 4 trays of cookies?

• 165

• 205

• 245

• 285

Answer explanation

The least number of cookies possible on 4 trays is 50 x 4 = 200 and the greatest number of cookies possible on 4 trays is 240 so our answer has to be between those two numbers.

• (-2, 0)

• (0, 5)

• (2, 1)

• (2, -1)

Answer explanation

If we plug in x and y in our equation, we'll have 0 < -4(-4) + 4 which is equivalent to 0 < 20, which is true.

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

• (0, 0)

• (-3, 0)

• (2, -5)

• (3, -1)

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

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 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 inequalities represent the situation?

• x + y ≥ 6
  32x + 20y ≤ 150

• x + y ≥ 632
  x + 20y ≥ 150

• x + y ≤ 6
  32x + 20y ≤ 150

• x + y ≤ 6
  32x + 20y ≥ 150