252 algebra De mystif ieD
Angela has grades of 78, 83, 86, 82, and 88. If the next grade counts twice
as much as each of the others, what does this grade need to yield an aver-
age of 85?
Even though there are a total of six grades, the last one counts twice as
much as the others, so it is like having a total of seven grades; that is, the
divisor needs to be seven. Let x represent the next grade.78 83 86 82 88 2
785417 2
7857417 2
77+ ++++=+ = +
=xxx (()85417 2 595
417 417
2 178
178
2+=
−
==xxxx== 89Angela needs a grade of 89 to raise her average to 85.A major project accounts for one-third of the course grade. The rest of the
course grade is determined by the quiz average. Allan has quiz grades of
82, 80, 99, and 87, each counting equally. What does the project grade
need to be to raise his average to 90?
The quiz average accounts for two-thirds of the grade and the project,
one-third.
The equation to use, then, is^23 quiz average +^13 project grade = 90. The quiz
average is82 80 99 87
4+++= (^87)