Question

A friend has a 83% average before the final exam for a course. That score includes everything but the final, which counts for 25% of the course grade. What is the best course grade your friend can earn? % What is the minimum score would your friend would need on the final to earn a 75% for the course? %

Answer 1

`\mathrm{Best\:course\:grade\:possible:\:}87.25\%,\\\mathrm{Minimum\:score\:on\:final\:to\:earn\:at\:least\:a\:75\%\:for\:the\:course:\:}51\%`

Explanation:

Assuming the maximum score for the final is
`100\%`, 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
`100\%`, their overall grade for the course would be:

`83(1-0.25)+100(0.25)=\fbox{$87.25\%$}`.

To find the minimum score they need to earn a 75% for the course, we set up the following equation:

`83(1-0.25)+x(0.25)=75`, where
`x` is the minimum score she needs.

Solving, we get:

`62.25+x(0.25)=75,\\x(0.25)=12.75,\\x=\fbox{$51\%$}`.