Question

You need at least 10,000 points to advance to the next level of a video game. Your current score is 4400 points. A. Write and solve an inequality that represents how many more points you need to advance. B. You find a treasure chest that increases your current score by 50%. How does this affect your answers in part a? ​

Answer 1

A) 4,400 + s ≥ 10,000

s ≥ 5,600

B) 4,400(1.5) + s ≥ 10,000

6,600 + s ≥ 10,000

s ≥ 3,400

Answer 2

To advance to the next level, a player initially needs at least 5,600 more points beyond their current 4,400 points. After finding a treasure chest that grants an additional 50% of their current points, they only need 3,400 more points to reach the 10,000-point goal.

Step-by-step explanation:

To answer part A, we need to establish an inequality to represent the points needed to advance to the next level in the video game. Since you currently have 4,400 points and you need a minimum of 10,000 points, the inequality to solve for the additional points needed, let's call them x, would be:

4400 + x ≥ 10000

Solving this inequality:

1. Subtract 4400 from both sides to isolate x: x ≥ 10000 - 4400
2. x ≥ 5600

This means you need at least 5,600 more points to advance to the next level.

For part B, if a treasure chest increases your current score by 50%, that means you earn an additional half of your current 4,400 points, which is 2,200 points. So your new score would be:

4400 + 2200 = 6600 points

The new inequality, since your score has increased, would be:

6600 + x ≥ 10000

And solving for x would now give us:

1. Subtract 6600 from both sides: x ≥ 10000 - 6600
2. x ≥ 3400

This means that after finding the treasure chest, you would need at least 3,400 more points to advance to the next level