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]
