Question

A student scored 75 and 97 on her first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive.

Answer 1

`85 \le (75 + 97 + n)/(3) \le 90`;
`83 \le n \le 98`

Explanation:

Score of the first two quizzes: 75 and 97

Let n represent the third score

Average score would be:
`(75 + 97 + n)/(3)`.

Given that the average score fall between 85 and 90, this can be represented by the compound inequality as shown below:

`85 \le (75 + 97 + n)/(3) \le 90`

Solve for n in each statement that makes up the compound inequality:

`85 \le (75 + 97 + n)/(3)`

`85 \le (172 + n)/(3)`

Multiply both sides by 3

`85*3 \le 172 + n`

`255 \le 172 + n`

Subtract 172 from each side of the inequality

`255 - 172 \le n`

`83 \le n`

Also,

`(75 + 97 + n)/(3) \le 90`

`(172 + n)/(3) \le 90`

Multiply both sides by 3

`172 + n \le 90*3`

`172 + n \le 270`

Subtract 172 from both sides of the inequality

`n \le 270 - 172`

`n \le 98`

Combining both together, the possible values of her third quiz score would be:

`83 \le n \le 98`