Question

D 2t + 0.75; $5.75A student scored 75, 81, and 76 in three out of the four math tests she has takenthis semester. If the student wants her average score in math to be at least 80,which inequality represents the range of the score (x) she needs to earn on thefinal math test?A 80 < x < 88B 80 < x < 88C 88 < X < 100D 88 < x < 100Which inequality correctly matches the graph?

Answer 1

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:

$\begin{gathered} \bar{score}=\frac{75+81+76+x}{4}>80 \\ \frac{232+x}{4}>80 \\ \frac{232+x}{4}\cdot4>80\cdot4 \\ 232+x>320 \\ x>320-232 \\ x>88 \end{gathered}$

The score of the fourth test has to be 88 or more. As the maximum score is 100, x has to be:

88