Question

a student scored 88, 89, and 91. what score must the student earn on the next exam to have an average above 90?​

Answer 1

More than 92.

Explanation:

Let
`s` be the mark of the student on the next exam.

What would be the average of the four exams?

The average mark is the sum of scores on the exams over the number of exams taken.

• The sum of the student's marks will be
  `88 + 89 + 91 + s = 178 + s`.

• The student would have taken four exams by then.

What would be the average?

`\text{Average} = (88 + 89 + 91 + s)/(4) = (178 + s)/(4)`.

What's the mark required for the next exam?

`\text{Average} > 90\\(178+s)/(4) > 90\\`

Multiple both sides by the denominator:

`(178 + s)/(4) * 4 > 90 * 4 \\178 + s > 90 * 4\\ 178 + s > 360 \\s > 360 - 178\\s > 92`.

Note the wording "an average above 90."

`s {\bf >} 92` "greater than" rather than
`s \ge 92` "greater than or equal to."