Grade computation problems are probably the most useful to students. In these problems, the formula for the course grade and all but one grade are 224 given. The student is asked to compute the unknown grade in order to ensure a particular course average.
Examples
A student
has grades of 72, 74, 82, and 90. What does the next grade have to be to obtain
an average of 80?
We will be taking the average of five
numbers: 72, 74, 82, 90 and the next grade. Call this next grade x. We want
this average to be 80.
The student
needs an 82 to raise his/her average to 80.
A student
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 be in order to yield an
average of 85?
Even though there will be a total of six
grades, the last one will count 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.
The student
needs a grade of 89 to raise the 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. A student has quiz grades of 82, 80,
99, and 87, each counting equally. What does the project grade need to be to
raise the student’s average to 90?
The quiz average accounts for two-thirds of
the grade and the project, one-third. The equation to use, then, is ⅔ quiz
average + ⅓ project grade = 90. The quiz
average is 
.
Let x represent the project grade.
The student
needs a grade of 96 for a course grade of 90.
Practice
1. A
student’s grades are 93, 89, 96, and 98. What does the next grade have to be to
raise her average to 95?
2. A
student’s grades are 79, 82, 77, 81, and 78. What does the next grade have to
be to raise the average to 80?
3. A
presentation grade counts toward one-fourth of the course grade. The average of
the four tests counts toward the remaining threefourths of the course grade. If
a student’s test scores are 61, 63, 65, and 83, what does he need to make on
the presentation grade to raise his average to 70?
4. The
final exam accounts for one-third of the course grade. The tion accounts for th
final third A student’s test scores are 68, 73, 80, and 95. His presentation
grade is 75. What does the final exam grade need to be to raise his average to
80?
5. A
book report counts toward one-fifth of a student’s course grade. The remaining
four-fifths of the courses’ average is determined by the average of six
quizzes. One student’s book report grade is 90 and has quiz grades of 72, 66,
69, 80, and 85. What does she need to earn on her sixth quiz to raise her
average to 80?
Solutions
1. Let
x = the next grade.
The
last grade needs to be 99 in order to raise her average to 95.
2. Let
x = the next grade.
The
next grade needs to be 83 to raise the average to 80.
3. Let
x represent the presentation grade. The test average is (61 + 63 + 65 + 83)/4
= 68. Then ¾ test average + ¼ presentation grade ¼ 70 becomes ¾ (68) + ¼ x =
70.
He
needs a 76 on his presentation to have a course grade of 70.
4. Let
x represent the final exam grade. The test average is (68 + 73 + 80 + 95)/4
== 79. Then ⅓ test average +⅓ presentation grade +⅓ final exam grade is 80
becomes,
The
final exam grade needs to be 86 to obtain an average of 80.
5. Let
x = sixth quiz grade. The course grade 4/5 quiz grade + 1/5 book report becomes,
Simplified,
the above is,
The
student needs a 93 on her quiz to raise her average to 80.
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