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Word Problems About Grade Help

By — McGraw-Hill Professional
Updated on Sep 27, 2011

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.

Increasing/Decreasing by a Percent Examples

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.

Increasing/Decreasing by a Percent Examples

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 Increasing/Decreasing by a Percent Examples quiz average + Increasing/Decreasing by a Percent Examples project grade = 90. The quiz average is Increasing/Decreasing by a Percent Examples

Let x represent the project grade.

Increasing/Decreasing by a Percent Examples

The student needs a grade of 96 for a course grade of 90.

Word Problems about Grade Practice Problems

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 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?
  4. 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?
  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

Increasing/Decreasing by a Percent Solutions

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

Increasing/Decreasing by a Percent Solutions

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

  1. Let x represent the presentation grade. The test average is (61 + 63 + 65 + 83)/4 = 68. Then Increasing/Decreasing by a Percent Solutions presentation grade = 70 becomes Increasing/Decreasing by a Percent Solutions

     

    Increasing/Decreasing by a Percent Solutions

    He needs a 76 on his presentation to have a course grade of 70.

  2. Let x represent the final exam grade. The test average is (68 + 73 + 80 + 95)/4 = 79. Then Increasing/Decreasing by a Percent Solutions presentation grade Increasing/Decreasing by a Percent Solutions final exam grade is 80 becomes

     

    Increasing/Decreasing by a Percent Solutions

    The final exam grade needs to be 86 to obtain an average of 80.

  3. Let x = sixth quiz grade. The course grade Increasing/Decreasing by a Percent Solutions quiz grade Increasing/Decreasing by a Percent Solutions book report becomes

     

    Increasing/Decreasing by a Percent Solutions

    Simplified, the above is

    Increasing/Decreasing by a Percent Solutions

    We want this quantity to equal 80.

    Increasing/Decreasing by a Percent Solutions

    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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