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?

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%.