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In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Paul has scored 75, 80, and 91 on the first three. What range of scores on the fourth test will give Paul a C for the semester (an average between 70 and 79, inclusive)? Assume that all test scores have a non-negative value.

Respuesta :

Answer:

Scores between 34 and 70 on the fourth test will give Paul a C for the semester.

Step-by-step explanation:

The average is given by the sum of all scores divided by the number of scores.

In this question:

Sum of all scores: 75 + 80 + 91 + x = 246 + x

Number of tests : 4

Grade of 70:

[tex]\frac{246 + x}{4} = 70[/tex]

[tex]246 + x = 280[/tex]

[tex]x = 280 - 246[/tex]

[tex]x = 34[/tex]

Grade of 79:

[tex]\frac{246 + x}{4} = 79[/tex]

[tex]246 + x = 316[/tex]

[tex]x = 316 - 246[/tex]

[tex]x = 70[/tex]

Scores between 34 and 70 on the fourth test will give Paul a C for the semester.

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