High School

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You need at least [tex]\$60[/tex] to buy a new video game. You have saved [tex]\$25[/tex]. Which inequality models how much more you must save?

A. [tex]n + 25 \leq 60[/tex]
B. [tex]n - 25 \geq 60[/tex]
C. [tex]n + 25 \geq 60[/tex]
D. [tex]60 + 25 < n[/tex]

Answer :

To figure out how much more you need to save to buy the video game, we can set up an inequality. Here’s how you can think through it step by step:

1. Identify the total amount needed: You need [tex]$60 to buy the video game.

2. Determine how much you have already saved: You have already saved $[/tex]25.

3. Determine how much more you need to save: Let’s use [tex]\( n \)[/tex] to represent the amount of money you still need to save.

4. Set up the inequality. You know that the amount you have saved plus the amount you need to save must be at least equal to [tex]$60. This can be modeled with the inequality:
\[
n + 25 \geq 60
\]

5. Solve the inequality for \( n \):
- Subtract $[/tex]25 from both sides of the inequality:
[tex]\[
n + 25 - 25 \geq 60 - 25
\][/tex]
- Simplify the expression:
[tex]\[
n \geq 35
\][/tex]

This means you need to save at least $35 more to buy the video game. So, the correct inequality is [tex]\( n + 25 \geq 60 \)[/tex].

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