Florida Teacher Certification Examinations (FTCE) Subject Area Practice Test

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What formula represents the new average of five scores when a sixth score of 100 is added?

5x + 100 / 6
(5x + 100) / 6
(5 + 100) / x
5 / (x + 100)

The correct answer is: (5x + 100) / 6

The correct answer is represented by the formula (5x + 100) / 6 because it accurately calculates the new average of the six scores. In this context, 'x' refers to the average of the original five scores. When you add the sixth score of 100 to these five scores, you effectively increase the total by 100. The expression 5x signifies the total value of the first five scores (since x is the average of these five scores, multiplying by 5 gives the total sum). By adding 100 to this total, we get 5x + 100, which represents the sum of all six scores. To find the new average, we then divide this total by the number of scores, which is now 6. Hence, the formula (5x + 100) / 6 provides the new average after incorporating the additional score of 100. Other formulas, like 5x + 100 / 6 or the others, do not accurately represent this scenario for various reasons. For instance, the placement of parentheses is crucial in mathematical operations, affecting the order of operations and subsequently the result; without proper grouping, the calculation may be misrepresented.