High School

Which inequality represents this situation?

Alicia has at most [tex]\$210[/tex] to buy a new tennis racket [tex](x)[/tex] and a new tennis net [tex](y)[/tex].

A. [tex]x + y \leq 210[/tex]
B. [tex]y \leq 210 + x[/tex]
C. [tex]x + y \geq 210[/tex]
D. [tex]y - x \leq 210[/tex]

Answer :

Sure, let's look at the situation step by step:

Alicia has at most [tex]$210 to spend on a new tennis racket and a new tennis net.

1. Assign Variables:
- Let \( x \) represent the cost of the tennis racket.
- Let \( y \) represent the cost of the tennis net.

2. Understand "at most" concept:
- "At most" $[/tex]210 means the total amount Alicia can spend on both items combined cannot exceed [tex]$210. So, the total cost of the racket and the net has to be less than or equal to $[/tex]210.

3. Formulate the Inequality:
- Since Alicia is buying both a racket and a net, the total cost can be represented by the expression [tex]\( x + y \)[/tex].
- Therefore, the inequality to represent this situation is [tex]\( x + y \leq 210 \)[/tex].

Thus, the correct inequality that represents this situation is:

(A) [tex]\( x + y \leq 210 \)[/tex].