Level Balance: Score Threshold Lab

Model score rules, solve inequalities, and graph the settings that work.

Build and Test Score Rules

Solve each problem. Counts of actions must be nonnegative whole numbers. Adjustable settings may be any real number unless stated otherwise.

A test level awards 18 starting points and 7 points for each checkpoint cleared. A player needs more than 60 points to unlock a bonus room. Let x be the number of checkpoints cleared. Which inequality models the requirement?

A. 18x + 7 > 60B. 7x + 18 > 60C. 7x + 18 ≥ 60D. 7x + 18 < 60

Another level starts a player with 35 points. Each energy cell collected adds 9 points. A special move unlocks only when the score is greater than 100.

What is the fewest number of energy cells the player must collect? cells

A test run begins with 92 points and loses 8 points per collision. The studio flags the run when its score falls below 52. Let x be the number of collisions. Which solution describes when the run is flagged?

A. The run is flagged when x > 5.B. The run is flagged when x < 5.C. The run is flagged when x ≥ 5.D. The run is flagged when x > 18.

A signed tuning setting x produces a score adjustment of 6x + 14 points. The studio wants the adjustment to be less than 2 points. Select every listed setting that meets the requirement.

A level's difficulty score starts at 12 and increases by 5 for each obstacle added. To stay in the beginner category, the difficulty score must be less than 49.

What is the greatest number of obstacles the designer can add? obstacles

Graph Adjustable Settings

In this section, x is a signed adjustable setting and may be any real number. Use an open circle for a boundary that is not included. Add an arrow to show the solution direction.

A level's balance rating is 4x + 6. The rating must be greater than −10. Solve 4x + 6 > −10 and graph all settings that meet the requirement.

A level's risk rating is −3x + 5. The rating must be less than 17. Which graph description represents all settings that work?

A. A filled circle at −4, shaded to the right.B. An open circle at −4, shaded to the left.C. An open circle at 4, shaded to the right.D. An open circle at −4, shaded to the right.

A level's challenge margin is −2x + 9 points. The margin must stay greater than 3 points. Solve −2x + 9 > 3 and graph all settings that meet the requirement.

The studio uses three different score rules. Match each requirement to the graph of its solution.

Make Balance Decisions

Use the inequalities to evaluate the studio's decisions. Pay attention to whether equality is allowed and whether x must be a whole number.

10.

A level starts at 20 points and awards 6 points per target hit. The bonus requires a score greater than 50. A tester says that hitting exactly 5 targets is enough. Which statement correctly checks the claim?

A. Five hits give 50 points, so the bonus unlocks.B. Five hits give 26 points, so the bonus stays locked.C. Five hits give 50 points, so the bonus stays locked.D. Five hits give 130 points, so the bonus unlocks.

11.

A player begins a challenge with 120 points and loses 7 points for each hint used. The player must finish with more than 65 points to earn a badge.

What is the greatest number of hints the player can use and still earn the badge? hints

12.

A reward currently requires 8x + 15 > 63, where x is the number of completed tasks. The studio wants a player who completes exactly 6 tasks to earn the reward. Which single change would make that happen?

A. Lower the required score from greater than 63 to greater than 62.B. Raise the required score from greater than 63 to greater than 65.C. Raise the required score from greater than 63 to greater than 64.D. Lower the starting score from 15 points to 14 points.

13.

A signed difficulty setting x produces a rating of 2.5x + 11. The studio requires the rating to be less than 28.5.

Complete the solution: x < .

14.

A level awards 12 starting points and 5 points per completed mission. One designer proposes a reward rule of 5x + 12 > 37. Another proposes 5x + 12 > 38. Here, x is a nonnegative whole number of completed missions. Will these rules reward exactly the same mission counts? Solve both inequalities and explain your reasoning.