<u><em>Answer:</em></u>
His overall grade is 81.9%
<u><em>Explanation:</em></u>
The easiest way to solve this question is by using simple cross multiplication.
<u>1- His overall percentage in exams:</u>
We are given that exams are worth 50% of the grade and that he scored an average of 82.2%
Assume that his overall percentage in exams is e
<u>We can setup the ratio and solve for e as follows:</u>
%
2- His overall grade in quizzes:
<u>We are given that quizzes are worth 30% of the grade and that he scored 74.4%</u>
Assume that his overall percentage in quizzes is q
<u>We can setup the ratio and solve for q as follows:</u>
%
<u>3- His overall grade in homework:</u>
We are given that homework is worth 15% of the grade and that he scored an average of 90%
Assume that his overall percentage in exams is h
<u>We can setup the ratio and solve for h as follows:</u>
%
<u>4- His overall grade in class participation:</u>
We are given that class participation is worth 5% of the grade and that he scored a 100% in it
Assume that his overall percentage in exams is p
<u>Since he scored 100%, then he scored the complete worth which is 5%</u>
p = 5%
<u>5- His overall grade in the course:</u>
The student's overall grade in the course is the summation of the above calculated percentages
<u>This means that:</u>
Overall grade = e + q + h + p
Overall grade = 41.1 + 22.32 + 13.5 + 5
Overall grade = 81.92% which is 81.9% approximated to one decimal place
Hope this helps :)