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Gail needs to earn a C in her Geology class. Her current test scores are 76, 72, 65, and 73. Her final exam is worth 3 test scores. In order to earn a C Gail's average must lie between 70 and 79 inclusive. What range of scores can Gail receive on the final exam to earn a C in the​ course?

Respuesta :

Answer:

Final test score should lie within the range of 21.33 and 36.33

Step-by-step explanation:

Given:

Test scores 76, 72, 65, and 73

Worth of final test score = 3

let the final test score be 'x'

thus,

Final test score = 3x

Now,

The average must lie between 70 and  79

i.e the minimum limit of average is 70 and maximum limit of average is 79

Also,

Average = [tex]\frac{\textup{Sum of all the test scores}}{\textup{Total number of test score}}[/tex]

or

Average = [tex]\frac{\textup{ 76 + 72 + 65 + 73 + 3x}}{\textup{5}}[/tex]

thus,

70 ≤  [tex]\frac{\textup{ 76 + 72 + 65 + 73 + 3x}}{\textup{5}}[/tex]  ≤ 79

or

70 × 5  ≤  [tex]\textup{ 76 + 72 + 65 + 73 + 3x}[/tex]  ≤ 79 × 5

350  ≤  [tex]\textup{ 286 + 3x}[/tex]  ≤ 395

or

350 - 286 ≤  [tex]\textup{ 3x}[/tex]  ≤ 395 - 286

or

64  ≤  [tex]\textup{ 3x}[/tex]  ≤ 109

or

21.33 ≤ x ≤ 36.33

Hence,

the final test score should lie within the range of 21.33 and 36.33

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