Keystone Algebra

Juan answered all 50 questions on a test. He earned 3 points for each question he answered correctly. He lost 1 point for each question he answered incorrectly. His final test score was 102 points. The system of equations below describes the relationship between the number of questions he answered correctly (x) and the number of questions he answered incorrectly ( y). x+y=50 3x-y=102 Part of the solution of the system of equations is x = 38. What does this value represent?

• the number of questions Juan answered correctly

• the number of questions Juan answered incorrectly

• the number of points Juan lost from questions he answered incorrectly

• the number of points Juan earned from questions he answered correctly

Jason decided that he will sell his stocks if their value per share (x) goes below $5 or above $15. Which compound inequality represents the values at which Jason will sell his stocks?

• x > $5 or x < $15

• x < $5 or x > $15

• x > $5 and x < $15

• x < $5 and x > $15

A ticket to a baseball game costs $20. Each soda sold at the game costs $5. Shawn may spend no more than $50. He buys 1 ticket and x sodas. Shawn represents this situation with the inequality below. 5x+20≤50 The solution of the inequality is x ≤ 6. Which statement best describes the solution of the inequality?

• Shawn buys 6 or fewer sodas.

• Shawn buys 6 or fewer tickets.

• Shawn buys 1 ticket and 5 sodas.

• Shawn has less than or equal to $6 remaining when he leaves the game.

A group of friends will buy at most 8 snacks at a movie theater and spend no more than $42. They will pay $4 for each box of candy and $7 for each bag of popcorn. The system of inequalities graphed represents this information.

Which combination of boxes of candy and bags of popcorn could the group buy?

• 2 boxes of candy and 6 bags of popcorn

• 3 boxes of candy and 4 bags of popcorn

• 5 boxes of candy and 4 bags of popcorn

• 8 boxes of candy and 1 bags of popcorn

• x = -2

• x = 0

• x = 1.5

• x = 9

• A

• B

• C

• D

One of the steps Lewis used to correctly solve an equation is shown below. Which statements describe the procedure Lewis used in this step of solving the equation and identify the property that justifies the procedure?

• Lewis added 3 and x to eliminate the parentheses. This procedure is justified by the associative property.

• Lewis added 3 and x to eliminate the parentheses. This procedure is justified by the distributive property.

• Lewis multiplied x and 7 by 3 to eliminate the parentheses. This procedure is justified by the associative property.

• Lewis multiplied x and 7 by 3 to eliminate the parentheses. This procedure is justified by the distributive property.

Raul has $640 saved, and Jaime has $320 saved. They each begin a new job on the same day and save all of their money. Raul earns $180 per day, and Jaime earns $200 per day. In how many days will they have an equal amount of money?

• 8

• 16

• 24

• 32

Patricia keeps apples in 3 bins and 2 crates in her store. Each bin can hold no more than 200 pounds. Each crate can hold no more than 50 pounds. Which graph represents all of the possible weights, in pounds, of apples Patricia can keep in her store?  

• A

• B

• C

• D

A band is determining how many songs to record for a new album. The band members want to record no more than 16 songs, and their album has to be shorter than 78 minutes. They can record short songs that are about 3 minutes in length or long songs that are about 5 minutes in length. Which system of inequalities best represents the number of short songs (x) and the number of long songs ( y) the band can record for the new album?