Keystone Algebra Prep

Juanita used the steps shown below to correctly solve an equation. A step is missing. Which shows the equation that is most likely a missing step and the property that justifies the step?

• -3c-6+4c=10c+9

  Associative property of addition

• -3c-6+4c=10c+9

  distributive property

• -3c+18+4c=10c+45

  distibutive property

• -3c+18+4c=10c+45

  associative property of addition

Christine sells a total of 50 tickets to a school play.  Student tickets sell for $1.50 each, and adult tickets sell for $4.00 each.  Christine made a total of $112.50 in ticket sales.  Christine writes a system of equations to represent this information.  Which statement best describes the solution to the system of equations. 

• Christine sells 35 student tickets and 15 adult tickets.  

• Christine would earn $200 by selling 50 adult tickets

• Christine sells a pair of tickets between $3 and $8

• Christine could not earn $112.50 by selling 50 student tickets.

A plain pizza takes 10 minuets to bake.  At least 2 minutes of baking time is required for each ounce of toppings added to the pizza.  The total baking time for specialty pizzas is at least 18 minutes and at most 26 minutes.  Which graph shows the possible number of ounces of all the toppings on specialty pizzas?

• A

• B

• C

• D

A cleaning service offers its customers a choice between the two plans.  
-Plan A costs $3000 and includes 1 year of unlimited cleanings
-Plan B costs $75 per cleaning
Henry wants to choose the less expensive plan.  He uses the inequality 3000<75c to deduce which plan to choose based on the number of cleanings (c) he expects to need.  Based on the solution of this inequality, which statement about Henry's choice of plan is true?

• Henry should choose plan A only if he expects to need fewer than 40 cleanings in 1 year.

• Henry should choose plan A only if he expects to need more than 40 cleanings in 1 year.

• Henry can choose either plan and pat the same amount if he expects to need fewer than 40 cleanings in 1 year.

• Henry can choose either plan and pay the same amount if he expects to need more than 40 cleanings in 1 year.

Kelly is planning a business trip to Hartford, CT and Boston, MA.  She is going to stay no more than 5 nights on the trip.  She estimates each night she stays at a hotel in Hartford will cost $90, and each night she stays at a hotel in Boston will cost $120.  She wants to spend no more than $540 for hotel stays.  Which graph represents the possible combinations of nights she can stay in Hartford (x) and nights she can spend in Boston (y)?

• A

• B

• C

• D

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

At the beginning of a road trip there are 14,000 miles on Denny's car.  During the trip, Denny drives his car at an average speed of 55 miles per hour.  Which graph best shows the total number of miles (y) on the car as a function of the number of hours (x) Denny drives at 55 miles per hour?

• A

• B

• C

• D

Edwin drove  261 miles from city X to Y in 4.5 hours.  He continues driving at the same average speed and drove another 145 miles from city Y to Z.  What is the total amount of time Edwin spent driving from city X to Z?

• 4.9 hours

• 6.3 hours

• 7 hours

• 9 hours

The graph below shows the relationship between the number of minutes (x) that have passed since an airplane began its decent and height above the ground (y), in feet, of the airplane.
Based on the graph, how long after it starts its decent will the airplane reach a height of 3,000 feet?

• 14 minutes

• 16 minutes

• 28 minutes 

• 32 minutes

The graph of a line is shown below:
What is the y-intercept of the line?

• -8/5

• -5/8

• 5

• 8