Answer:
[tex]\mathrm{Best\:course\:grade\:possible:\:}87.25\%,\\\mathrm{Minimum\:score\:on\:final\:to\:earn\:at\:least\:a\:75\%\:for\:the\:course:\:}51\%[/tex]
Step-by-step explanation:
Assuming the maximum score for the final is [tex]100\%[/tex], we can multiply each score by its respective course weight and add them together to give a final score. If your friend did receive this maximum score of [tex]100\%[/tex], their overall grade for the course would be:
[tex]83(1-0.25)+100(0.25)=\fbox{$87.25\%$}[/tex].
To find the minimum score they need to earn a 75% for the course, we set up the following equation:
[tex]83(1-0.25)+x(0.25)=75[/tex], where [tex]x[/tex] is the minimum score she needs.
Solving, we get:
[tex]62.25+x(0.25)=75,\\x(0.25)=12.75,\\x=\fbox{$51\%$}[/tex].
