Creating Equations and Systems

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5
  x+y=87

• 1.5x+0.5y=78.5
  1.5x+0.5y=87

• x+y=78.5
  1.5x+0.5y=87

• x+y=78.5
  x+y=87

Which system of inequality is shown?

• y > -1/5x - 1/2   and  y ≥ -2x - 4

• y > -1/5x - 1/2  and  y ≤ -2x - 4

• y ≥ -1/5x - 1/2   and  y ≤ -2x - 4

• y < -1/5x - 1/2   and  y ≥ -2x - 4

Which system of inequality is shown?

• y > -4/5x - 1 and y ≤ 2/3x + 3

• y ≥ -4/5x - 1 and y ≤ 2/3x + 3

• y < -4/5x - 1 and y < 2/3x + 3

• y < -4/5x - 1 and y ≥ 2/3x + 3

Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

• x+y=134
  x+y=120

• 3x+3y=134
  4x+3y=120

• 4x+3y=134
  3x+3y=120

• 7xy=134
  6xy=120

• A
• B
• C
• D

Find the exact real solutions to the system

• no real solutions

• (0, 5)

• (-10, 11)

• (5, 0)

Find the solution(s) to the system.

• (0,-3)(1,-2)

• (0,-3)

• (-2,0)(2,0)

• No solution

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

Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. There are $20 dollar bills and $50 dollar bills. How many of each bill does Caitlin have?
WRITE a system where T= # of $20 and F = # of $50.

• T + F = 1430
  20T + 50F = 49

• T+ F = 49
  10T + 5F = 1430 

• T + F = 49
  20T + 50F  = 1430

• T + F = 49
  T + F = 1430

Write the inequalities represented in the picture.

• y > -2 + x
  y ≤ 2x + 2

• y > 2 + x
  y ≤ 2x + 2

• y ≥ -2 + x
  y ≤ 2x + 2

• none of these are the system