The student have 3 scores and we want to calculate the range of values of the fourth test in order to have a average of 80 or more.
The test scores are 75, 81 and 76. We call x the fourth score.
Then, we can write the inequality to have at least an average of 80 as:
[tex]\begin{gathered} \bar{score}=\frac{75+81+76+x}{4}>80 \\ \frac{232+x}{4}>80 \\ \frac{232+x}{4}\cdot4>80\cdot4 \\ 232+x>320 \\ x>320-232 \\ x>88 \end{gathered}[/tex]The score of the fourth test has to be 88 or more. As the maximum score is 100, x has to be:
88
