**Answer:**

**(a) The student need 82 points on the final to average 74.**

**(b) The student must score 41 points on the final, assuming that the final carries double the weight.**

**Step-by-step explanation:**

We are given that a student's grades in the three tests in College Algebra are 85, 60, and 69.

**As we know that the formula for calculating the average of numbers is given by;**

Average (Mean) =

**(a) **Let the points student need on the final test to average 74 be ''.

So, Average of all four test =

**Hence, the student needs 82 points on the final to average 74.**

**(b) **It is given that the final carries double the weight, this means that let the points student need on the final test to average 74 be ''.

So, Average of all four test =

= 41

**Hence, the student must score on the final 41 points, assuming that the final carries double the weight.**