Question

After taking 9 tests, Carol's average grade in her

Italian class is 90. Her teacher drops the lowest of
the 9 test scores to determine the final grade. If
Carol's final grade is 91, what was her lowest test
score?

Answer 1

82

Explanation:

Given

Average in 9 tests = 90

Average when lowest score is removed = 91

Required

Find the lowest test score

Average or Mean is calculated as thus;

`Average = \frac{\sum x}n`

Where
`\sum x` is the sum of test scores

n = number of tests

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When the smallest scores is removed; n = 9 - 1 = 8 and average = 91

`Average = \frac{\sum x}n` becomes

`91 = \frac{\sum x}8`

Multiply both sides by 8

`8 * 91 = \frac{\sum x}8 * 8`

`8 * 91 = \sum x`

`728 = \sum x`

This means that Carol's test score in 8 subjects is 728

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Considering all 9 subjects

Let the 9th subject represent the subject Carol had the least score

n = 9

Average = 90

`\sum x` = 728 + the 9th subject

`Average = \frac{\sum x}n` becomes

`90 = (728\ +\ 9th\ subject)/(9)`

Multiply both sides by 9

`9 * 90 = (728\ +\ 9th\ subject)/(9) * 9`

`9 * 90 = 728\ +\ 9th\ subject`

`810 = 728\ +\ 9th\ subject`

Subtract 728 from both sides

`810 - 728 = 728\ - 728\ +\ 9th\ subject`

`82 = 9th\ subject`

Hence, Carol lowest test score was 82