Algebra Keystone Review

A baker makes two types of doughnuts.  It costs $0.25 to make each glazed doughnut and $0.30 to make each chocolate doughnut.  The baker wants to  make more than 200 doughnuts for the day but can spend no more than $60.00 making them.  The system of inequalities below describes the relationship between the number of glazed doughnuts (x) and chocolate doughnuts (y) the baker could make for the day.
0.25x+0.30y≤60.00
x+y>200
One solution of the system of inequalities is the ordered pair (100,110).  Which statement best describes the meaning of the solution?

• The baker could make 100 glazed doughnuts and 110 chocolate doughnuts
• The baker could earn $100 from glazed doughnuts and $110 from chocolate doughnuts
• The baker can make a maximum of 100 glazed doughnuts and 110 chocolate doughnuts
• The baker will spend exactly $60 making 100 glazed doughnuts and 110 chocolate doughnuts

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.

Simplify
(1/3)(21m + 27)

• 63m + 9
• 7m + 9
• 7m + 81
• 7m + 27

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

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

Solve for p.
5p - 14 = 8p + 4

• -6
• -10/3
• 18/13
• 4

What is the domain for {(1,2) (2,3) (3,4) (4,5)}?

• {1,2,3,4}
• {2,3,4,5}
• {1,2,3,4,5}
• {(1,2) (2,3) (3,4) (4,5)}

The table shows Eli’s distance from home as he rides his bike at a steady rate after meeting a friend. . Write an equation in y = mx + b form that represents the miles, y, that Eli goes in x hours. 

• y = 2x + 2
• y = 12x + 12
• y = 12x + 2
• y = 2x + 12

Which of the following could be a possible line of best fit for the data?

• y = 3x + 0
• y = 5/6x + 490
• y = -2x + 470
• non linear

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