John earn scores of 82%, 74%, and 78% on three mid-term tests in his Math
course. To earn a B, his overall course mark needs to be at least 80% and less than
90%. The overall course mark is 1
3
(mid-term average) plus 2
3
of the final
examination. In what range of values can his score on the final exam be so that he
has a B average?
The overall course mark is 1
3
(mid-term average) plus 2
3
of the final
examination.
Is this what you mean?
The overall course mark is 1/3 (mid-term average) plus 2/3 for the final examination.
To find the range of values for John's score on the final exam so that he has a B average, we need to calculate his overall course mark.
Let's start by calculating his mid-term average:
Mid-term average = (82% + 74% + 78%) / 3 = 78%
Next, we need to calculate his overall course mark using the mid-term average and the final examination score. We know that the overall course mark is calculated by taking 1/3 of the mid-term average and adding 2/3 of the final examination score.
Overall course mark = (1/3) * Mid-term average + (2/3) * Final examination score
Now we can substitute the given values to find the range of values for the final examination score.
80% ≤ Overall course mark < 90%
Let's substitute the given values to get the equation for the range:
80% ≤ (1/3) * 78% + (2/3) * Final examination score < 90%
To simplify the equation, we can multiply both sides by 3:
240% ≤ 78% + 2 * Final examination score < 270%
Simplifying further, we get:
240% - 78% ≤ 2 * Final examination score < 270% - 78%
162% ≤ 2 * Final examination score < 192%
Now we can isolate the Final examination score:
162% / 2 ≤ Final examination score < 192% / 2
81% ≤ Final examination score < 96%
Therefore, John's score on the final exam needs to be within the range of 81% to 95% for him to have a B average in the course.