Keystone Algebra Practice Questions

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A person’s hair is 8 centimeters long. The equation below can be used to estimate the length (L), in centimeters (cm), that the person’s hair will be after w weeks. Based on the equation, what will be the estimated length of the person's hair after 10 weeks?

• 4.5 cm

• 8 cm

• 10 cm

• 10.5 cm

Ms. Bernard monitored the growth of a fish. The fish originally weighed 27 ounces. The fish grew at a rate of 5 ounces per month. The equation below can be used to describe the weight, in ounces, of the fish. 72=27+5x Ms. Bernard correctly determined that x = 9. What does the solution of the equation mean?

• The fish grew at a rate of 9 ounces per month for 72 months.

• The fish grew at a rate of 72 ounces per month for 9 months.

• It took 9 months for the fish to grow to a weight of 72 ounces.

• It took 72 months for the fish to grow to a weight of 9 ounces.

A system of equations is shown below. What is the solution of the system of equations?

• (-2. -7)

• (2, 7)

• (2, 3)

• (3, 2)

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

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