Algebra 1 Keystone Prep

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.

The greatest common factor (GCF) of 2 monomials is 3x²y.  One of the monomials is 3x⁴y.  Which could be the other monomial?

• 3xy²

• 6x²y³

• 9x⁶y²

• 18x⁶y²

Simplify: 
(3x²+8x-8)-(-x²+6x+4)

• 2x²+8x-4

• 2x²+8x-12

• 4x⁴+8x-4

• 4x²+2x-12

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

• 5

• -3

• 0

• 1

Juanita used the steps shown below to correctly solve an equation. A step is missing.

-3(c-6)+4c=5(2c+9)

?

c+18=10c+45

c-27=10c

-27=9c

-3=c

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

Sylvia studied a new language.  The equation below describes how many words she knew (y) after studying the language for x days.
y=5x+18
The ordered pair (6,48) is a solution of the equation.  What does the solution represent?

• Sylvia knew 6 words after 48 days.

• Sylvia knew 6 words after 6 days

• Sylvia knew 48 words after 6 days

• Sylvia knew 48 words after 48 days

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.