We need that the average is at least 84.6 points. Let x be the score of the final test, the average then will be:
[tex]\frac{95+72+83+86+x}{5}=\frac{x+336}{5}[/tex]And we need this to be at least 84.6, this can be written as:
[tex]\frac{x+336}{5}\ge84.6[/tex]Now we solve this inequality to find x:
[tex]\begin{gathered} \frac{x+336}{5}\ge84.6 \\ x+336\ge84.6\cdot5 \\ x+336\ge423 \\ x\ge423-336 \\ x\ge87 \end{gathered}[/tex]Therefore John has to achieve at least 87 points in the fifth test to achieve an average of 84.6.
