Answer:
82
Step-by-step 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;
[tex]Average = \frac{\sum x}n[/tex]
Where [tex]\sum x[/tex] 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
[tex]Average = \frac{\sum x}n[/tex] becomes
[tex]91 = \frac{\sum x}8[/tex]
Multiply both sides by 8
[tex]8 * 91 = \frac{\sum x}8 * 8[/tex]
[tex]8 * 91 = \sum x[/tex]
[tex]728 = \sum x[/tex]
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
[tex]\sum x[/tex] = 728 + the 9th subject
[tex]Average = \frac{\sum x}n[/tex] becomes
[tex]90 = \frac{728\ +\ 9th\ subject}{9}[/tex]
Multiply both sides by 9
[tex]9 * 90 = \frac{728\ +\ 9th\ subject}{9} * 9[/tex]
[tex]9 * 90 = 728\ +\ 9th\ subject[/tex]
[tex]810 = 728\ +\ 9th\ subject[/tex]
Subtract 728 from both sides
[tex]810 - 728 = 728\ - 728\ +\ 9th\ subject[/tex]
[tex]82 = 9th\ subject[/tex]
Hence, Carol lowest test score was 82
