An instructor counts homework as 1/3 of the student's grade and the final exam to be 2/3 of the student's final grade. Going into the final exam a student has a homework grade of 48%. What range of scores on the final exam would put the student's final average between 70% and 80% inclusive if the instructor does not round off grades?
What is the range of the final exam scores?
1/3 of 48=16 points
He wants a 80 or 70
He needs 64 to 54 more points
so he needs to get on his final exam
3/2*64 to 3/2*70
Probability
To find the range of scores on the final exam that would put the student's final average between 70% and 80% inclusive, we can set up an equation using the weights of the homework and the final exam.
Let's denote the score on the final exam as 'x'. Since the homework is worth 1/3 of the student's grade, we need to multiply the homework grade (48%) by 1/3 to get its weight in the final average:
Homework weight = 48% * 1/3 = 16%
Now, we can calculate the weight of the final exam by multiplying 'x' by 2/3:
Final exam weight = x * 2/3
To find the final average, we need to add the homework weight and the final exam weight and then divide by the total weight:
Final average = (Homework weight + Final exam weight) / (1/3 + 2/3) = (16% + x * 2/3) / 1
Now, we can set up the inequality to determine the range of scores on the final exam:
70% ≤ (16% + x * 2/3) / 1 ≤ 80%
To simplify, we can multiply both sides of the inequality by 1 to get:
70% ≤ (16% + x * 2/3) ≤ 80%
Next, we can subtract 16% from all sides of the inequality:
54% ≤ x * 2/3 ≤ 64%
To get rid of the fraction, we can multiply all sides by 3/2:
(54% * 3/2) ≤ x ≤ (64% * 3/2)
Simplifying further:
81% ≤ x ≤ 96%
Therefore, the range of scores on the final exam that would put the student's final average between 70% and 80% inclusive is 81% to 96%.