Equations and Inequalities STAAR Algebra

A student is ordering a flower arrangement. She can choose any combination of roses and carnations for her flower arrangement, and she does not want to spend more than $30.

If roses cost $3 each and carnations cost $2 each, which inequality represents all possible combinations of x roses and y carnations?

• 3x + 2y < 30

• 3x + 2y ≤ 30

• 2x + 3y < 30

• 2x + 3y ≤ 30

Baseball fans can buy tickets for seats in the lower deck or upper deck of the stadium. Tickets for the lower deck cost $42 each. Ticket prices for the upper deck are 75% of the cost of tickets for the lower deck. Which inequality represents all possible combinations of x, the number of tickets for the lower deck, and y, the number of tickets for the upper deck, that someone can buy for no more than $800?

• 42x + 56y ≤ 800

• 42x + 31.5y ≤ 800

• 42x + 56y > 800

• 42x + 31.5y > 800

A family will travel 350 miles from their house in order to reach Dallas, TX. Which inequality can be used to find all possible values of t, the time it will take this family to reach Dallas in hours, if they travel at an average speed of at least r miles per hour?

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Which inequality can be represented by the graph?

• y ≥ x + b

• x - y ≥ -b

• x + y ≤ b

• -y ≤ x + b

A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of song that the drummer wrote. They wrote a total of 46 songs. Which system of equations models this situation if the drummer wrote d songs and the guitarist wrote g songs?

• g = 2d - 8

  g + d = 46

• g = 8 - 2d

  g = 46 - d

• d = 2g - 8

  d = 46 - g

• d = 8 - 2g

  d + g = 46

Which system of equations is best represented by this graph?

• 3x - y = 2

  4x + 9y = 36

• 3x - y = 6

  4x + 9y = 4

• x - 3y = -18

  9x + 4y = 9

• x + y = 10

  9x + 4y = 13

A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. Which system of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?

• 0.10q + 0.25d = 2.85

  q + d = 18

• 0.10q + 0.25d = 18

  q + d = 2.85

• 0.25q + 0.10d = 2.85

  q + d = 18

• 0.25q + 0.10d = 18

  q + d = 2.85

A new spiral notebook contains 30 more sheets of paper than a new memo book. The total number of sheets of paper in 3 new spiral notbooks and 5 new memo books is $810. Which system of equations can be used to find s, the number of spiral notebook, and m, the number of sheets of paper in one new memo book?

• s - m = 30

  3s + 5m = 810

• s + m = 30

  3s + 5m = 810

• s - m = 30

  5s + 3m = 810

• s + m = 30

  5s + 3m = 810

Which graph represents the solution of y≥ -7x - 2

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Which ordered pair is in the solution set of y ≥ ⅓x + 4

• (-6, 1)

• (-1, 6)

• (6, -1)

• (1, -6)