**Word Problems About Grades**

**Finding the Grade Needed to get a Specific Average Grade**

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 given. The student is asked to compute the unknown grade in order to ensure a particular course average.

**Examples**

**Example 1:**

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.

**Example 2:**

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.

**Example 3:**

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 quiz average + 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.

**Word Problems about Grade Practice Problems**

**Practice**

- A student’s grades are 93, 89, 96, and 98. What does the next grade have to be to raise her average to 95?
- 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?
- A presentation grade counts toward one-fourth of the course grade. The average of the four tests counts toward the remaining three-fourths 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?
- The final exam accounts for one-third of the course grade. The average of the four tests accounts for another third, and a presentation accounts for the 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?
- 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**

The last grade needs to be 99 in order to raise her average to 95.

The next grade needs to be 83 to raise the average to 80.

- Let
*x*represent the presentation grade. The test average is (61 + 63 + 65 + 83)/4 = 68. Then presentation grade = 70 becomesHe needs a 76 on his presentation to have a course grade of 70.

- Let
*x*represent the final exam grade. The test average is (68 + 73 + 80 + 95)/4 = 79. Then presentation grade final exam grade is 80 becomesThe final exam grade needs to be 86 to obtain an average of 80.

- Let
*x*= sixth quiz grade. The course grade quiz grade book report becomesSimplified, the above is

We want this quantity to equal 80.

The student needs a 93 on her quiz to raise her average to 80.

Practice problems for this concept can be found at: Algebra Word Problems Practice Test.

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