Constraints System of Linear Equations

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

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. What is the maximum profit?

• $47,400
• $49,200
• $51,000
• $52,300

What is the solution to this system of equations?

• (4, -1)
• (-1, 4)
• (-4, 1)
• (-4, -1)

A gym charges a one-time registration fee as well as a monthly fee. The cost of joining the gym for 4 months is $370, and the cost of joining for 6 months is $530. Write a system of equations to find the registration fee and monthly fee. m= months; r = registration fee.

• r - 4m = 370
  r - 6m = 530
• r + 4m = 370
  r + 6m = 530
• m + 4r = 370
  m + 6r = 530
• m - 4r = 370
  m - 6r = 530

Diego scores 11 more points than Travis.  Together they score 21 points.  How many points did each person score?

• Diego: 11,   Travis: 10
• Diego:  10,  Travis:  11
• Diego: 5,  Travis:  16
• Diego:  16, Travis:  5

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

• $5
• $10
• $15
• $20

In a pasture are horses and chickens if there are a total of 28 animals and 80 legs how many chickens and horses?

• 10 horses, 18 chickens
• 16 horses, 12 chickens
• 12 horses, 16 chickens
• 18 horses, 10 chickens

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3
• x + y = 33
  x = 2y - 3
• x + y = 33
  x = 3 - 2y
• x + y = 3
  x = 33 - 2y

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)
• (-1,-3)
• (-1,3)
• (3,1)