In his mathematics class, John has taken 3 tests, each worth 20% of his total grade. His grades on those tests were 92%,83%,and 85%. He has an 100% average on his homework, worth 10% of his grade. All that remains is a final exam worth 30% of his total grade. To the nearest percent what must he make in the final exam to have a 90% average in the class?
so far he has
.2(92+83+85) + 10
= 62
let his mark on the final be x
62 + .3x = 90
.3x = 28
x = 93.3
To find out what John must score on his final exam, we can break down his current average and the desired average.
Currently, John's average consists of the following components:
- 3 tests, each worth 20% of his total grade
- Homework, worth 10% of his grade
The sum of these components is equal to 100%:
Current Average = (Test 1 + Test 2 + Test 3) / 3 * (20%) + Homework * (10%)
John's goal is to have a 90% average at the end of the course. This average should also consist of the following components:
- Current average (70%)
- Final Exam, worth 30% of his total grade
Thus, the equation becomes:
Desired Average = Current Average * (70%) + Final Exam * (30%)
90% = (Test 1 + Test 2 + Test 3) / 3 * (20%) + Homework * (10%) + Final Exam * (30%)
Now, we can plug in the known values and solve for the Final Exam score.
Test 1 = 92%, Test 2 = 83%, Test 3 = 85%, Homework = 100%
90% = (92% + 83% + 85%) / 3 * (20%) + 100% * (10%) + Final Exam * (30%)
Next, we simplify the equation:
90% - (92% + 83% + 85%) / 3 * (20%) - 100% * (10%) = Final Exam * (30%)
Now, we can calculate the value on the left-hand side:
90% - (92% + 83% + 85%) / 3 * (20%) - 100% * (10%) ≈ 56.33
Finally, we can solve for the Final Exam score by rearranging the equation:
Final Exam ≈ (90% - 56.33) / (30%)
Final Exam ≈ 11.23
Therefore, to have a 90% average in the class, John must score around 11.23% on his final exam, rounded to the nearest percent.