Writing Systems of Equations and Inequalities

The owner of Mark's Meat Market orders beef and chicken. He wants to but at least 50 pounds of meat but cannot spend more than $300. Beef is $3 a pound and chicken is $2 a pound.
Which system of inequalities models this situation?

• x + y $\le$ 50
  2x + 3y $>$ 300

• x + y $\ge$ 50
  3x + 2y $\le$ 300

• x + y $<$ 300
  2x + 50 $\ge$ 300

• x - y $\le300$
  3x + 2y $\le$ 50

A radio station is giving away tickets to a concert. There are $10 tickets and $20 tickets. They want to give away at least 20 tickets but want to spend at most $280.

Let x = the number of $10 tickets

Let y = the number of $20 tickets

Which system of inequalities models the situation?

• x + y $\ge$ 20
  10x + 20y $\le$ 280

• x - y $\ge$ 20
  20x + 10y $\le$ 280
  

• x + y $\ge$ 280
  10x + 20y $\le$ 20

• x + y $<$ 20
  10x + 20y $>$ 280

Joe bought 2 pairs of jeans and 1 shirt for $120. Sam bought 1 pair of jeans and 3 shirts for $135. What are the two unknowns in this problem?

• the number of pair of jeans and shirts
• the price of a shirt and a pair of jeans
• the total price Sam and Joe paid
• the total number of shirts and jeans that Sam and Joe brought

You are hosting family and friends for dinner. There will be at least 8 people attending. You will prepare some vegetarian dinner that cost $5 and a meat-based dinner that costs $6. You hope to spend no more than $70.

Let x = number of vegetarian dinners

Let y = number of meat-based dinners

Which system that could represent this situation?

• x + y $\le$ 70
  5x + 6y $\le$ 70

• 5x + 6y $\le$ 10
  x + y $\ge$ 70

• x - y $\ge$ 7
  x + y $\le$ 6

• x + y $\ge$ 8
  5x + 6y $\le$ 70

You have a total of 17 coins.  All of your coins are nickels and dimes.  The total value of the coins is $1.35.  Which system of equations represents this situation?

• n+d=17
  .05n+.10d=1.35
• .05n+.10d=17
  n+d=1.35
• .25n+.10d=1.35
  n+d=17

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

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

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

At a restaurant, the cost for 2 burritos and 1 tortilla salad is $20.57. The cost for 3 burritos and 3 tortilla salads is $36.24. Which pair of equations can be used to determine b, the cost of a burrito, and t, the cost of a tortilla salad?

• b + t = 20.57

  
  

  3b + 3t = 36.24

• 2b + t = 20.57

  
  

  3b + 3t = 36.24

• 2b + t = 20.57

  
  

  b + t = 36.24

• b + 2t = 20.57

  
  

  b + t = 36.24

Westlake Catalog sells mavericks jerseys for $39 and Rangers hats for $18. Megan orders "j" jerseys and "h" hats. The total numbers of items ordered is 25, and the total cost is $702. Which system of equations represent this situation?

• j = 39

  
  

  h = 18

• j + h = 25

  
  

  j + h = 702

• j + h = 25

  
  

  39j + 18h = 702

• j + h = 702

  
  

  39j + 18h = 25