Couple of Confusing Problems

Question

40 students signed up to take the California Math League exam. 2 of the students got sick

and missed the exam. The remaining students got an average of 89%. The two sick students

took the make-up exam and scored 99% each. What is the average score of the class on the

exam?

A bag of candy is given to the 10 member 4th grade and 5th grade math team where each

student receives 6 candies. If the candies are given to the 5th grade math team only, each

student receives 10 candies. If the candies are given to the 4th grade math team only, how

many candies will each student receive?

Answer 1

38x89= 3382

3382/38=89 = average

then 2 got 99 each

new average for all 40=

(3382+2(99))/40=89+99/20= 89+4.95= 93.95 looks about right, intuitively

but that's 3382/38 + 198/40=93.95

= (3382+198)/40= 3580/40= 358/4= 89.5 inuition is wrong

arithmetic mean = average= sum of all grades/number of grades= sum/n=3580/40=89.5= correct new average

2 99's bumped the average up 1/2 a point