In `his(1)` `course(1)` class, `person(1)` took `LENGTH` `plural(exam(1))`. `His(1)` scores were `toSentence(SCORES)`.

What was `his(1)` average score on the `plural(exam(1))`?

The average is the sum of `his(1)` scores divided by the number of scores.

There are `LENGTH` scores and their sum is

.`SCORES.join(" + ")` = `SUM`

`His(1)` average score is

.`SUM` \div `LENGTH` = `SUM / LENGTH`

On the first `COUNT` `plural(exam(1))` of `his(1)` `course(1)` class, `person(1)` got an average score of `OLD_AVG`.

What does `he(1)` need on the next `exam(1)` to have an overall average of `NEW_AVG`?

Let `his(1)` score on the next `exam(1)` be `x`

.

The sum of all of `his(1)` scores is then

.`COUNT` \cdot `OLD_AVG` + x

The same sum must also be equal to

.`COUNT + 1` \cdot `NEW_AVG`

Solve: `x = `

.`COUNT + 1` \cdot `NEW_AVG` - `COUNT` \cdot `OLD_AVG` = `(COUNT + 1) * NEW_AVG - COUNT * OLD_AVG`

`person(1)` has taken `COUNT` `plural(exam(1))` and `his(1)` average score so far is `OLD_AVG`.

If `he(1)` gets 100, a perfect score, on the remaining `REMAINING` `plural(exam(1))`, what will `his(1)` new average be?

If `he(1)` gets 100 on the remaining `plural(exam(1))`, the sum of `his(1)` scores will be

.`COUNT` \cdot `OLD_AVG` + `REMAINING` \cdot `100` = `COUNT * OLD_AVG + 100 * REMAINING`

`His(1)` overall average will then be

.`COUNT * OLD_AVG + 100 * REMAINING` \div `COUNT + REMAINING` = `NEW_AVG`