Marks average for all 14 quizzes was an 81. Mark had an average of 75 for his first 10 quizzes, what was the average score for his last 4 quizzes?

Question

Please solve and explain the process without guess and check.

Answer 1

Remember that:

    average = (sum of values) / (count of values)

 

So, (sum of values) = (count of values)*average

 

For 14 quizzes, Mark's average was an 81   means

      (14-quiz sum) = 14*(14-quiz average)

      (14 quiz sum) = 14*81 = 1134

 

For 10 quizzes, Mark's average was 75

      (10-quiz sum) = 10*75 = 750

 

Now,

  14-quiz average is:

      (14-quiz sum) / 14  = 81

      (10-quiz sum + 4-quiz sum) / 14 = 81

      (10-quiz sum + 4-quiz sum)  = 81*14  = 1134        [multiply both sides by 14]

           (750 + 4-quiz sum = 1134

              4-quiz sum = 384

        (4-quiz average) = (4-quiz sum) / 4 = 384 / 4 = 96

 

Now, this is the same as two tests -- one weighing 1400 points and one weighing 400 points):

      score 75% of 1000 (actually 10 quizzes) and x% of 400

           750 + 400x = 14*81

           750 + 400x = 1134

                     400x = 384

                        x = 0.96 = 96%