Keystone Review Algebra

The equation below describes the relationship between the number of months (x) since a customer began renting a storage unit and the total amount of money (y), in dollars, the customer has paid to the storage facility.

y = 15x + 30

Which statement describes a solution of the equation based on the number of months the customer has rented the storage unit?

• After exactly 16 months, the customer has paid $240.

• After exactly 240 months, the customer has paid $16.

• After exactly 16 months, the customer has paid $270.

• After exactly 270 months, the customer has paid $16.

Charlene owns a bookstore. She purchases used books from customers.

• She pays $3.50 for each hardback book.

• She pays $0.75 for each paperback book.

• Charlene pays a customer a total of $199.75 for 149 used books.

Which system of equations could be used to determine the number of hardback books (x) and the number of paperback books (y) Charlene purchases from the customer?

• x + y = 199.75

  0.75x + 3.50y = 149

• x + y = 149

  0.75x + 3.50y = 199.75

• x + y = 199.75

  3.50x + 0.75y = 149

• x + y = 149

  3.50x + 0.75y = 199.75

A part for a machine must meet certain length requirements, in centimeters (cm), as shown in the inequality below.

|6.75 – x| < 0.25

Which statement completely describes the length requirements for this machine part?

• The length of the part must be less than 7 cm.

• The length of the part must be greater than 6.5 cm.

• The length of the part must be less than 6.5 cm or greater than 7 cm.

• The length of the part must be greater than 6.5 cm and less than 7 cm.

Which of the following systems of inequalities is graphed?

• 2x - 1 ≤ 3

  2x + 3 ≥ 11

• 2x - 1 ≥ 3

  2x + 3 ≤ 11

• x - 1 ≥ 3

  x + 3 ≤ 10

• 0 ≥ 3 + x

  3x -1 ≤ 11

All the books in a bookstore window display today will be mysteries and biographies. The system of inequalities below describes the relationship between the number of mysteries (x) and the number of biographies (y) that could be in the display.

x + y ≤ 30

2x ≤ 3y

Which description is a possible number of books of each type that could be in the display?

• 6 mysteries and 22 biographies

• 15 mysteries and 8 biographies

• 21 mysteries and 14 biographies

• 24 mysteries and 12 biographies

Small baskets of tomatoes are sold at a vegetable stand for $3 per basket. Large baskets of tomatoes are sold at the stand for $5 per basket. Only whole numbers of baskets may be purchased. A customer purchases a total of 8 baskets of tomatoes and pays $36. Write and solve a system of equations that models the number of small baskets (x) and the number of large baskets (y) that the customer purchases.

• x + y = 36

  3x + 5y = 8

  3 small baskets

  4 large baskets

• x + y = 8

  3y + 5x = 36

  6 small baskets

  2 large baskets

• x + y = 8

  3x + 5y = 36

  2 small baskets

  6 large baskets

• 5x + y = 8

  3y + x = 36

  6 small baskets

  2 large baskets

Kyle has $4 more than twice as much money as Lana. Lana has x dollars. Kyle does not have enough money to buy a video game that costs $56, but he has enough money to buy a textbook that costs $38. Write a compound inequality that represents all the possible amounts of money Kyle could have in terms of x.

• 38 ≤ 2x + 4 < 56

• 38 > 2x + 4 >56

• x > 26 and x <17

• 38 < x < 56

The following inequality represents the amount of money lana can make per hour (x):

38 ≤ 2x + 4 < 56

Which pay rate for Lana will satisfy the inequality?

• $13/ hour

• $26/ hour

• $18/ hour

• $33/ hour

Which set of ordered pairs is a function?

• {(-10, 4), (-8, 3), (-8, 2), (-4, 1)}

• {(-2, 4), (0, 4), (2, 4), (2, 6)}

• {(1, 5), (1, 6), (2, 7), (3, 8)}

• . {(-1, 1), (0, 0), (1, 1), (2, 2)}

In an experiment, a plant grows 0.05 centimeters per day.  The plant had a height of 2 centimeters when the experiment started.  Which equation describes the relationship between the number of days (d) the experiment lasts and the height (h), in centimeters, of the plant?

• h=0.05d+2
• h=0.05(2)+d
• h=2d+0.05
• h=2.05d