Question

In a class in which the final grade depends entirely on the average of four equally weighted 100- point tests, frank has scored 79,75, and 88 on the first three. What range of scores on the fourth test will give frank a c for the semester (an average between 70 and 79, inclusive) ? Assume that all test scores have a non - negative value.

Answer 1

In order to determine the range of scores, let x the score of the fourth test.

Use the limits of the interval at which frank obtains a c for the semester, then, you can write for an average score of 70:

`\begin{gathered} (79+75+88+x)/(4)=70 \\ 242+x=4\cdot70 \\ 242+x=280 \\ x=280-242 \\ x=38 \end{gathered}`

and for an average score of 79:

`\begin{gathered} (79+75+88+x)/(4)=79 \\ 242+x=4\cdot79 \\ 242+x=316 \\ x=316-242 \\ x=74 \end{gathered}`

The previous results for x determines the range of values of the scores frank can obtain to get a c.

The range of values is in between 38 and 74