Pattering and Algebraic Reasoning Practice

Amira is saving money for a new phone that costs $800. She already has $200 saved and plans to save $50 each week.Create an equation to represent how much money Amira will have saved after w weeks. How many weeks will it take for her to have enough to buy the phone?

Jordan needs at least 40 hours of community service for graduation. He already has 10 hours and can volunteer 3 hours each weekend. Write and solve an inequality to determine how many weekends, w, he needs to volunteer to meet the requirement.

Emma earns $15/hour at her part-time job and works h hours per week. Write an expression to represent her weekly earnings. Then, determine how much she’ll earn if she works 12 hours.

A cell phone company charges a $25 activation fee and $40 per month. Write an equation for the total cost, C, after m months. How much will it cost after 6 months?

A park rents canoes for $10 per hour with no additional fees. The graph below represents the cost of renting a canoe. Which of the following statements about the graph is true?

• The relationship is proportional because the line passes through the origin.

• The relationship is non-proportional because there is a flat fee.

• The slope of the line is 0 because the cost does not change.

• The graph is non-linear because the cost increases unevenly.

Answer explanation

The graph passes through the origin and increases at a constant rate. This means the cost is directly proportional to the time.

A gym charges a one-time fee of $50 to join and $30 per month afterward. This situation is shown on a graph. Which equation best models the cost, C, in dollars, after m months?

• C = 30m

• C = 50m + 30

• C = 30m + 50

• C = 80m

Answer explanation

The cost includes $50 upfront and $30 each month. This is a non-proportional relationship because it does not pass through the origin.

Alex and Nina are comparing pay from two different jobs:

• Alex: $12/hour (no starting bonus)

• Nina: $10/hour and a $20 signing bonus

• Which explanation correctly explains the graph's appearance when comparing their earnings over time?

• Both lines start at the origin and Alex’s line is steeper.

• Nina’s line starts at 0 and is steeper than Alex’s.

• Alex’s line starts at the origin; Nina’s line starts higher but is less steep.

• Both lines are horizontal.

Answer explanation

The slope of the line shows the rate of change—in this case, 4 gallons per minute.

A tank is being filled at a constant rate of 4 gallons per minute. The graph of the situation starts at (0, 0). What does the slope of the graph represent?

• The number of minutes before the tank starts filling.

• The total amount of water in the tank.

• The constant rate of water being added per minute.

• The maximum capacity of the tank.

Answer explanation

The slope of the line shows the rate of change—in this case, 4 gallons per minute.