Solving/interpreting linear inequalities in two variables

Ms. Loredo is making her special cantaloupe-and-honeydew salad for a family gathering she is hosting and does not want to spend more than $30 at the supermarket. Currently, cantaloupes cost $3 each and honeydew melons cost $2 each. Which inequality in slope-intercept form best represents the number of cantaloupes, x, and honeydew melon, y. (Write an inequality first, then solve for y.)

• $y<-\frac{3}{2}x+15$

• $y\le-\frac{3}{2}x+15$

• $y\le\frac{3}{2}x+15$

• $y\ge-\frac{3}{2}x+15$

A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per week. His goal is to make at least $300 per week.

Which system of equations or inequalities model the situation?

• 15x + 20y > 20

  x + y        < 300

• 15x + 20y > 300

  x + y     < 20

A farmer has a field that can be used to grow two types of crops, corn and wheat. Each acre of corn requires 2 hours of labor and each acre of wheat requires 3 hours of labor. The farmer has a total of 40 hours of labor available. The farmer wants to grow at least 5 acres of corn and at least 8 acres of wheat. Write a system of linear inequalities to represent this situation.

• 2x + 3y >= 40, x <= 5, y <= 8.

• 2x + 3y <= 40, x <= 5, y <= 8.

• 2x + 3y >= 40, x >= 5, y <= 8.

• 2x + 3y <= 40, x >= 5, y >= 8

• x = 0, y = 300

• x = 150, y = 150

• x = 100, y = 150

• x = 150, y = 100

Tags

A2.ACE.3

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

• Lewis can use six 50-cent stamps and four 23-cent stamps.

• Lewis can use five 50-cent stamps and five 23-cent stamps.

• If Lewis uses six 50-cent stamps, he only needs to use two 23-cent stamp.

• If Lewis uses fourteen 23-cent stamps, he only needs to use one 50-cent stamp.

JoAnn likes her job as a baby-sitter (b), but it pays only $3 per hour. She has been offered a job as a tutor (t) that pays $6 per hour.
Because of school, her parents only allow her to work a maximum of 15 hours per week, but she needs to make at least $66 per week. Which system of inequalities below correctly models Joann's situation?

• b + t < 15
  3b + 6t > 66
• b + t > 15
  3b + 6t < 66
• 3b + 6t > 15
  b + t < 66
• 3b + 6t < 15
  b + t < 66

A farmer has asked you for advice on the best strategy for planting wheat and corn on her 500-acre farm. To make it through harvest time, each acre of wheat she plants will require 1 person-day of labor and other expenses of $20. Each acre of corn she plants will require 5 person-days of labor and expenses of $30. The farmer has $11,400 and 1480 person-days of labor available, and she expects to make a profit of $90 per acre of wheat and $120 per acre of corn. If x = acres of wheat and y = acres of corn, which of the following is NOT a constraint?

• x + y ≤ 500
• 20x + 30y ≤ 11,400
• y ≥ 5x + 30
• x + 5y ≤ 1480

Find the optimal point and optimal value with the objective "maximise  $P=2x+y$ " 

• Optimal point:  $\left(37.5,\ 22.5\right)$ 
   Optimal value:  $97.5$  

• Optimal point:  $\left(16\frac{2}{3},\ 10\right)$ 
   Optimal value:  $43\frac{1}{3}$  

• Optimal point: $\left(38.5,\ 24.5\right)$ 
   Optimal value:  $101.5$  

• Optimal point:  $\left(41.5,\ 25.5\right)$  
   Optimal value:  $105.5$  

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 (x) $7 and a pizza costs (y) $13.

7x + 13y ≤ 81

Given Ms. Savva's budget, which of the following give a viable option she can purchase for the school party?

• 7 breadstick and 3 pizzas

• 3 breadstick and 4 pizzas