randRange(4, 6) randRange(75, 98, LENGTH) sum(SCORES)

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

In her course(1) class, person(1) took `LENGTH` plural_form(exam(1), LENGTH). Her scores were toSentenceTex(SCORES).

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

What was her average score on the plural_form(exam(1))?

SUM / LENGTH

The average is the sum of his scores divided by the number of scores.

The average is the sum of her scores divided by the number of scores.

There are `LENGTH` scores and their sum is `SCORES.join(" + ") = SUM`.

His average score is `SUM \div LENGTH = SUM / LENGTH`.

Her average score is `SUM \div LENGTH = SUM / LENGTH`.

randRange(3, 7) randRange(77, 88) randRange(OLD_AVG + 2, 99) NEW_AVG + COUNT * (NEW_AVG - OLD_AVG)

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

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

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

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

ANS

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

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

The sum of all of his scores is then `COUNT \cdot OLD_AVG + x`.

The sum of all of her scores is then `COUNT \cdot OLD_AVG + x`.

The same sum must also be equal to `COUNT + 1 \cdot NEW_AVG`.

So, `COUNT \cdot OLD_AVG + x = COUNT + 1 \cdot NEW_AVG`

`\begin{eqnarray} COUNT \cdot OLD_AVG + x &=& COUNT + 1 \cdot NEW_AVG \\ COUNT * OLD_AVG + x &=& (COUNT + 1) * NEW_AVG \\ x &=& (COUNT + 1) * NEW_AVG - COUNT * OLD_AVG \\ x &=& ANS \\ \end{eqnarray}`

randRange(3, 6) randRange(2, COUNT - 2) randRange(77, 88) COUNT * OLD_AVG + 100 * REMAINING SUM / (COUNT + REMAINING)

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

person(1) has taken `COUNT` plural_form(exam(1), COUNT) and her average score so far is `OLD_AVG`.

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

If she gets `100`, a perfect score, on the remaining `REMAINING` plural_form(exam(1), REMAINING), what will her new average be?

NEW_AVG

If he gets `100` on the remaining plural_form(exam(1)), the sum of his scores will be `COUNT \cdot OLD_AVG + REMAINING \cdot 100 = SUM`.

If she gets `100` on the remaining plural_form(exam(1)), the sum of her scores will be `COUNT \cdot OLD_AVG + REMAINING \cdot 100 = SUM`.

His overall average will then be `SUM \div COUNT + REMAINING = NEW_AVG`.

Her overall average will then be `SUM \div COUNT + REMAINING = NEW_AVG`.