Question

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?

Answer 1

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

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 =
`\frac{\textup{Sum of all the test scores}}{\textup{Total number of test score}}`

or

Average =
`\frac{\textup{ 76 + 72 + 65 + 73 + 3x}}{\textup{5}}`

thus,

70 ≤
`\frac{\textup{ 76 + 72 + 65 + 73 + 3x}}{\textup{5}}` ≤ 79

or

70 × 5 ≤
`\textup{ 76 + 72 + 65 + 73 + 3x}` ≤ 79 × 5

350 ≤
`\textup{ 286 + 3x}` ≤ 395

or

350 - 286 ≤
`\textup{ 3x}` ≤ 395 - 286

or

64 ≤
`\textup{ 3x}` ≤ 109

or

21.33 ≤ x ≤ 36.33

Hence,

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