Jenny earned a 77 on her most recent test. Jenny's score is no less than 5 points greater than [tex]\frac{4}{5}[/tex] of Terrance's score. If [tex]t[/tex] represents Terrance's score, which inequality represents the situation?

A. [tex]77 \ \textgreater \ 5 + \frac{4}{5} t[/tex]
B. [tex]77 \geq 5 + \frac{4}{5} t[/tex]
C. [tex]77 \ \textless \ 5 + \frac{4}{5} t[/tex]
D. [tex]77 \leq 5 + \frac{4}{5} t[/tex]



Answer :

Let's break down the problem step by step:

You know that Jenny's score is 77. It's given that Jenny's score is no less than 5 points greater than [tex]\(\frac{4}{5}\)[/tex] of Terrance's score.

Let's denote Terrance's score by [tex]\(t\)[/tex].

First, express the statement "5 points greater than [tex]\(\frac{4}{5}\)[/tex] of Terrance's score" mathematically:
[tex]\[ 5 + \frac{4}{5}t \][/tex]

The problem also states that Jenny's score (77) is "no less than" this value. Mathematically, "no less than" translates to "greater than or equal to (≥)".

So, you set up the inequality:
[tex]\[ 77 \geq 5 + \frac{4}{5}t \][/tex]

Therefore, the inequality that represents this situation is:
[tex]\[ \boxed{77 \geq 5 + \frac{4}{5}t} \][/tex]