In a particular class, exams are worth 50% of the overall grade, quizzes are worth 30% of the overall grade, homework is worth 15% of the overall grade, and class participation is worth 5% of the overall grade.
a particular student has earned an average score of 82.2% on the exams, 74.4% on the quizzes, 90.0% on the homeworks, and 100.0% on class participation. what is this student's overall grade in the course?
report the answer with one digit after the decimal point.

His overall grade is 81.9%

Explanation:

The easiest way to solve this question is by using simple cross multiplication.

1- His overall percentage in exams:

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

We can setup the ratio and solve for e as follows:

%

2- His overall grade in quizzes:

We are given that quizzes are worth 30% of the grade and that he scored 74.4%

Assume that his overall percentage in quizzes is q

We can setup the ratio and solve for q as follows:

%

3- His overall grade in homework:

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

We can setup the ratio and solve for h as follows:

%

4- His overall grade in class participation:

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

Since he scored 100%, then he scored the complete worth which is 5%

p = 5%

5- His overall grade in the course:

The student's overall grade in the course is the summation of the above calculated percentages

This means that:

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 :)