In the first four papers, each of 100 marks, Henrich got 65, 70, and 60 marks. If he wants an average of marks between 65 and 70, find the range of marks he should get in the fifth paper.

To find the range of marks Henrich should get in the fifth paper, we first need to calculate the total marks he has obtained in the first four papers.

Total marks obtained = 65 + 70 + 60 = 195

Now, to find the average marks he needs to achieve between 65 and 70, we can calculate the average of 65 and 70:

Average = (65 + 70) / 2 = 135 / 2 = 67.5

To maintain an average between 65 and 70, Henrich needs to have a total of 270 marks for all five papers.

Now, we can calculate the range of marks he should get in the fifth paper:

Minimum marks = 270 - 195 = 75
Maximum marks = 270 - 195 + 100 = 175

Therefore, Henrich should aim to get between 75 and 175 marks in the fifth paper to maintain an average between 65 and 70.

Step 1: Calculate the current average

Average = (65 + 70 + 60) / 3 = 65

Step 2: Determine the range of marks needed for an average between 65 and 70

Let n be the marks Henrich gets in the fifth paper.

For an average between 65 and 70, we have:

65 < (65 + 70 + 60 + n) / 4 < 70
Simplifying:
255 + n < 280
n < 25

Conclusion:

Henrich should get between 0 and 24 marks in the fifth paper to achieve an average between 65 and 70, inclusive.