THE SCORES OF BOTH TESTS ARE AVERAGED. 

That means a first-test score of 71 and a retake-test score of 96 averages to 83.5%, which I will round up to 84%.  There are some variations to this, however.  Please read these:
 
POLICY 1: if a student does really poorly the first time, such as 38%, it would normally be almost impossible to get an average above D, so I will temporarily raise the first test score to 60% only for the purpose of averaging.  EXAMPLE: a student who earns 38% for a first-test then learns it much better and earns 94% on the retake-test will then have a final score of 77%, C (that's the average of 60 and 94). 

POLICY 2: any student may retake a test regardless of the score, but I will cap any final averaged score at 90%, A-.  EXAMPLE: a student who earns 86% on the first-test then earns 100% on the retake-test will receive a final score of 90%, A-, not the actual average of 93.
 
POLICY 3: The retake test is meant to help students' scores, NEVER to hurt their score.  Thus, if they do worse on the retake test, they score does NOT go down.  They get to keep the original score since it is higher than the retake test's score.  Example:  a student scores 62%, D on the first test, but only 54%, F on the retake test.  The average would be 58%, F, but since I won't use a retake score if it's lower then the first test, the original 62% score will stay in the grade book and is the final score.  NOTE: there is only one retake test, so if a student scores lower on the retake test, the student has used up the one opportunity to raise the score.
 
POLICY 4: If a student earned a 20% penalty for not taking the test on time, that 20% penalty applies to the retake test also.  EXAMPLE: a student who earns 74% on the first-test actually really earns 54%.  I will count that 54% as 60% for averaging (following policy 1 above).  If the student then earns 98% on the retake-test, that score is lowered to 78%, and then the 78% and 60% are averaged together for a final score of 69%, D.  Obviously, it does not pay to take a test late in my class (unless there is a true emergency; parents can talk to me when there's an emergency and I'll waive the penalty).