josephs final averages in science class are shown in the table below.
homework
% toward final grade-20%
average-93
quizzes
% toward final grade-20%
average-92
tests
% toward final grade-40%
average-85
final exam
% toward final grade-20%
average-?
what is the minimum score joseph can get on the final exam in order to receive at least 90 for his final grade?
.2*93 + .2*92 + .4*85 + .2*X >= 90. Solve for X.
95
To find the minimum score Joseph can get on the final exam in order to receive at least a 90 for his final grade, we can use the concept of weighted averages.
First, let's calculate the overall weighted average of Joseph's grades before the final exam. We will multiply each average by the corresponding weight:
- Homework weight: 20% = 0.20
- Homework average: 93
- Quizzes weight: 20% = 0.20
- Quizzes average: 92
- Tests weight: 40% = 0.40
- Tests average: 85
- Final exam weight: 20% = 0.20
- Final exam average: ?
To calculate the overall weighted average, we sum the products of each average and its corresponding weight:
Overall weighted average = (homework average * homework weight) + (quizzes average * quizzes weight) + (tests average * tests weight) + (final exam average * final exam weight)
Now, let's set up an equation to find the minimum score Joseph can get on the final exam:
90 = (93 * 0.20) + (92 * 0.20) + (85 * 0.40) + (final exam average * 0.20)
Simplifying the equation:
90 = 18.6 + 18.4 + 34 + (final exam average * 0.20)
Rearranging the equation to solve for the final exam average:
(final exam average * 0.20) = 90 - (18.6 + 18.4 + 34)
(final exam average * 0.20) = 90 - 71
(final exam average * 0.20) = 19
Finally, solving for the final exam average:
final exam average = 19 / 0.20
final exam average = 95
Therefore, Joseph needs to score at least 95 on the final exam in order to receive at least a 90 for his final grade.